That is a tough one!! Maybe you should go with your gut feelings and the fact that you are feeling 'sick' when you think of giving him away. You should trust your feelings, they are so important. They might not just be from your wanting him to stay, they might also be about what is best for him.
Is he bonded with your other cats or friends with one or two of them? I have 9 cats and some of them are very close with each other. Would another one of your cats be left feeling sad if he were to leave?
Also, since you now know what she is looking for, maybe you could help her find another cat of the same description in the pound or on petfinder and that cat will get a home since Amos already has one?
But if you do decide that you want to give him a home with her, maybe you could arrange for her to 'test drive' him for a week. If it's not working out or if he is depressed, he could come back?