I find it really really weird that there is a waiting list to have a cat neutered. It's only takes a day and it's so routine.. are you specifically calling low cost places?

As for another home, if you are afraid that he's going to run away, wouldn't you rather know where he ends up? You are right to be concerned that he might try to find your old house. Have you thought about an outdoor pen? Does your new home have a backyard? I know there are a few people on here that have an outdoor pen for their kitties to play in in the summers or if they are involved in rescue. If you did it that way, you could make sure he's not partaking in the nightlife, if you know what I mean, and he would be safe. Would you parents let you build something like that?