Does your rescue agency cover the fees for an emergency vet visit? It might make you feel better if you can take him to one tonight. Just slide him onto the car seat on the blanket he's on now to prevent jolting him.

He may be swallowing a lot because they intubated him and his throat is sore. Since spay takes longer, I think they give an anethestic shot and then intubate, whereas for a quick neuter, they can just use gas in a face mask - someone correct me if I am wrong here. Or he could be swallowing because he's nauseated, and that can cause a cat to produce a lot of saliva.

What a horrible experience for you both. No, you are not over-reacting, I'd be very concerned also.

I'm going to put a new thread in Cats General telling people to check out this one and give responses. That forum is read far more often than this one and I don't want you to miss out on help from our very experienced posters.