Ratsicles, I'm going to do what I can to answer each point. Keep in mind, I'm not fond of long posts, LOL.
We found Punchy (APBT) on the side of the road on, I think, October 15th. Vet placed him at about 10 weeks, so he's going on 4 months now.
My first thought was that it's possible the vet made an estimate that could be off by a week perhaps. Thus, you could have picked him up at the tail end of the socialization window, so even though you did what you could, the window was closing fast. With a dog that is genetically predisposed to shyness, or one that has had almost no contact with humans, you could face a daunting remedial socialization project. Kim's suggestions make a lot of sense in that context.
It has become very, very obvious that he got probably zero human contact before we found him. He is terrified of people. He warmed up to DH and I very quickly, and he isn't afraid of us, except when we ask him to "Come." He knows the command, so that isn't the issue- he's just scared to do it. If I just show him a treat, or if I call one of the other dogs, he comes running.
You say he comes when he sees a treat...are you certain he knows the command, or just sees the treat and realizes that you will give it to him. You may have fallen prey to accidentally bribing the little guy, rather than reinforcing.
If I call him specifically, he seems to WANT to come, but for some reason it's just too scary. He'll get all wiggly, put his ears back, make appeasement gestures with his paws, and even try some whiney barks- but he will NOT come.
Don't try to make him come from across the room. Make it easier, so that he is successful every time. Wait until he is fluent in one circumstance before upping the difficulty level. Grab "Really Reliable Recall", Leslie Nelson's DVD and teach him that way, since he is obviously food motivated. It's the same method, with a few minor changes, that I use on my own dogs, all of whom come when called - even my shy Sioux, who hid under the chairs at her first puppy class;-) Yup, my ace therapy dog was once a weenie of sorts herself.
If I keep calling him, he'll eventually run and hide and cower.
Simple - don't do that. If you have to call more than once, you are simply training your dog that the word "come" can be ignored. As I said, get the DVD - I think it will help.
I don't know why, we NEVER call our dog's names in anger, or call them when they're in trouble, so he has no reason to fear us calling his name or asking him to "come." And he doesn't seem afraid of coming in general if there is food involved, or if one of the other dogs is coming...
so I'm really not sure if this is actual fear, or him just not wanting to come. From his body language, it certainly SEEMS like fear.
I always make sure my body language is non-threatening when I call
him- I crouch down, and I turn away from him- so that shouldn't be the
issue.
I'm guessing that you may have messed up the mechanics of making him understand the request, or been too obvious with your food lure, or used it too long. He probably feels safer following the lead of a more confident dog, too. I don't think he fears you per se, but I do think he gets confused, and confusion leads to - you guessed it - fear.
So far, we've just been clicking/treating whenever he comes up to us, whether we call him or not, and making a big huge fuss/clicking and treating when he does come when we call...but it's been about a month and he still hasn't gotten it. For the record, he housetrained in 3 days, and learned every other command I've tried to teach him in 10-15 minutes- so he definitely understands the process and is a really smart dog. He just honestly seems afraid when one of us calls his name. 
That's really a minor thing though, the main reason for this post is this- he is TERRIFIED of new people. We've been socializing him like crazy, but I can almost guarantee that he literally had NO human contact before we found him- it's a long story, but we're pretty sure we know where he came from and it isn't good. I'm willing to bet that when I grabbed him off the side of the road, it was the first time a human ever touched him. Seriously.
He warmed up to Josh and I and except for the issue we're having with getting him to come when we call him, he acts totally normal around us. Not really fearful at all. He's smart, he's well behaved, he plays nicely with the other dogs, he even has the most amazing bite inhibition I've ever seen with a puppy his age- he almost NEVER mouths. He's very well socially adjusted...with dogs. With humans, he's terrible.
I would not force people on him. What I would do is to feed him liverwurst when a human that he doesn't know appears. When the human leaves, the food disappears. All you are trying to do is change his perception about humans, using classical conditioning. Later, you can progress to having a dog savvy human toss a treat on the floor toward him, or allow him to come up and sniff (at his own pace, don't put the hand out toward him initially). This can be a long, painstaking process for a dog that is really terrified, and the notion of using an anti-anxiolytic drug is not altogether a bad one in some cases, while behavior modification protocols are started.
We had him vetted almost immediately after we found him and started taking him everywhere. For the past month and a half, we've been taking him to Petco, Petsmart, the park, or friends houses literally every day. I think we've missed maybe 3 days since we've had him. He is getting socialization out the wazoo...and it doesn't seem to be making a difference.
When people come up to pet him, he cowers and hides. If I happen to be holding him, he tries to hide his face in my shirt. If he's walking, he wraps himself around my legs and tries to get behind me. Tail tucked, shaking, whites of his eyes showing, drooling, absolute terror. Once someone starts petting him he'll start to wag a little, so it seems like he WANTS to enjoy it...but he's too afraid.
We've made sure he's had no negative interactions with people. If people want to pet him, we explain that he has some fear issues, but that he doesn't bite, we tell them how to approach him and make SURE they do it correctly, and we always have them offer him treats. He's generally too scared to take the treats.
If he's too scared to take the treats, you are going too fast. I know that you think he's had no negative interactions with people, but if you think about it, he's had to go to strange places, and have those scary beings touch him and make life even scarier. Try feeding him yourself when the people appear. If he will take treats from you, keep feeding as long as there are people nearby, but don't worry yet if they are not feeding him. Change the perception first.
If someone comes over to our house, he runs and hides the second he hears the car pull up, and doesn't come out until they're gone. When he acts terrified, we DON'T try to console him or give him any attention for it...we ignore him. If people ignore him every time they come over, he will accept them and start interacting with them after a few visits.
That's great!!!! If he is accepting them, wonderful. It's fine to ignore him rather than console him, but I'd rather have you feeding him for being in the room with the humans if he will take food from you. (Don't use Cheerios - the appearance of strange humans should signal liverwurst, turkey, roast beef...something great that he never gets any other time.)
After about 3 weeks of seeing my parents twice a week, he now is fine with them...so he CAN get over having strangers in the house, but my main thing is wanting him to be okay with people coming up to him out in public.
He's NOT fear aggressive...but he's also very young. Right now he just tries to hide, but I really worry about this turning into fear aggression- and a fear aggressive pit bull is not a good thing to have.
My guess is that if he is not aggressive now, he will not suddenly get aggressive later, unless something really, really scary happens and he's cornered. He sounds like the type that will retreat if he can, rather than get testy.
We tried clicking/treating whenever he is calm and accepts handling from people out in public, which is what worked wonders on Ogre's fear aggression when we first got him...but Punch is generally too scared to take treats, so it doesn't really work.
Again, change the perception first. If people predict liverwurst, they are a lot less scary when they come a bit closer. But, if the appearance of a human always means that he will be touched against his will, I'm not sure how much progress you will make. With a terrified dog, I like to let the dog make the first overture. Have a friend sit on the floor with liverwurst bits all around him. Have the human remain still, and let the dog go for the gold if he wants, but if he doesn't, don't force it. The overture was there, and he learned that the human was not going to do anything scary.
I just worry about him growing up terrified of people, and I have NEVER seen a puppy as young as him that was this frightened of strangers. It concerns me that in a month and a half we've seen ZERO progress in how he accepts strangers...maybe I'm not being patient enough?
I think you are simply dealing with a very socially retarded puppy, and are overfacing him a bit.
Pit bulls just don't need any more bad press...I want him to grow up to be a friendly, social, well behaved bully ambassador...not a fear aggressive mess that will reaffirm people's negative ideas about the breed.
I'm guessing that he will not be a fear aggressive mess, just a fearful dog that hides when company comes. He doesn't have to be an ambassador, he just has to keep his nose clean.
Do you guys think he's doomed to a life of being terrified of strangers? Could it just be something that he'll grow out of, or is there something different that I should be doing?
I would attempt to increase his general confidence level. Agility training helps some dogs a lot, and I would also grab two books specifically designed to help owners deal with shy dogs. "The Cautious Canine" (Patricia McConnell) and "Help for Your Shy Dog" (Deborah Wood). Both have great suggestions for increasing your dog's ability to deal with real life.
He is such an awesome, sweet little guy. I would hate for him to miss out on alot of fun in life. because he can't get over his fear of strangers.
Me, too. But, he already got lucky landing with someone who cares enough to help him. So, he's headed in the right direction.