I just want to pass on some ideas for your consideration.
You may be able to borrow a live trap from Animal Ark, set it up with liver and other smelly appealing treats, IF you can figure out where he is within a few miles. The folks at Animal Ark have live traps they do lend out. Last I knew, they handle their live traps through their thrift store, so you could try that first. (651) 772-8983. One obstacle is that the shop is in St. Paul, but I'm betting someone from the cities who is volunteering to help might bring it down to the area. Bigger obstacle is that the trap will need to be checked often overnight if it will be cold outside, so the dog doesn't get hypothermic inside it.
Meanwhile, in the daylight hours, if some of your searchers could carry some good-smelly food with them it might attract him more quickly. We were told that liver scents travel quite far.
You've probably thought of all this, but I'm just thinking back to the early days when we were looking for a dog who went missing this time last year, and the things we were trying to get in place or ready to use "just in case".
Hudson WI animal control also has a live trap they lend out, but I'm not sure how far they will let it travel. I believe it is big enough for a 50-pound dog, if I recall correctly. Again, someone would have to pick it up and return it. (715) 386-4771
Perhaps some animal shelter or authority closer to where you are would lend some items, like slip collars for searchers to carry, treats or food, live traps. They did recommend we set up a feeding station AND this one they said...
It is important - if you can get in the general vicinity of where the dog has been, leave something out with it's owners' or at least a familiar scent on it - a jacket or the dog's blanket or hay the dog has slept on or something warm would be great.
I realize you think this might be over before those items could be shipped to the searchers, but in case this goes on for days and days, think about what you want to use, if time were no object, and have someone get it to you. (I wish I were closer so I could come and help search. I am in Michigan right now.)
I'll post other links and ideas as I think of them. I will go through my old notes and see what other contacts we were making.
Is there a better place to get this info to you, than here? I've noticed this seems to have some updated info, thus why I'm posting here. I also e-mailed you through Craigslist (I'm the one who thought I might be able to find the police officer with the tracking dog - but that didn't pan out) however, the woman is letting some friends in the area where the dog was lost, so you might hear from them as volunteers too. Keep getting the word out and ask for what you need. People are amazing and will come out of the woodwork to try to help in situations like this, as you are already finding out!
I'm keeping Godzilla and all the searchers in my thoughts and prayers, and sending "stay safe" and "stay close" vibes to him!!!
The above is not meant as advice - I'm surely no expert - but just passing along ideas we were given early in our search for your consideration. Certainly; depending on what else is going on in the area - traffic; people; etc. - will determine if any of the ideas are feasible or safe; etc.