Awwwww, I could hug you for doing this for him. I know he is sad, stressed, and doesn't know what the heck is going on, but stand strong and don't let him back out, or you will NEVER catch him again. He doesn't understand now, but he will. I am hoping that he has already been neutered too, am holding out hope that is the case.
That is awesome that you found a cat only vet! And one that sounds great too, that is perfect. If I didn't have faith in the vets that I have and had to look for another one, I would find one that just does cats too. Sounds like they really know what they are doing and that they have cats best interest at heart.
Maybe after tomorrow you can let him out in the basement, hopefully he can't find his way out of there or into anything and hurt himself trying to get out. I would almost want to keep him in the dog crate until Friday, because if he isn't neutered, you are going to have one tough time getting him back in there. Maybe if you go down there and just talk quietly to him, offer him something really yummy, like tuna or a fishy canned food, maybe he will want that.
Maybe once you find out if he is neutered or not, they can ear tip him if he is, in case it doesn't work out with him being inside, then hopefully animal control would leave him alone or someone else that finds him doesn't go through this ordeal you are going through. And I get what your husband is thinking, if it doesn't work out him being inside, and he has to live outside, it will be obvious that he is neutered with the ear tip. Does your basement have a door that leads to outside? I am not familiar too much with basements, I'm in FL, so sorry if that is a stupid question, I just know my dads basement has a door that leads to outside, and I was thinking if yours did, maybe he could have a cat door and go in and out? Even if he ends up being an outside cat, you will have done so much for him by getting his shots up to date, and making sure he can't make more baby kitties. He may surprise you though, after living his rough life outdoors, he may be quite happy to become a house kitty. But if not, and he has to live outside, he will still be so much better off. Thank you for caring for this poor little guy.