Thanks for the input guys!
At the moment, I'm not sure where else I would put his tub... So I may have to try it for a few weeks, see how it goes, then move the boa somewhere else if I have to. In this case, there really are disadvantages to having a free-roaming predator as a pet. The only other room he's not allowed in during the day is our bedroom, but he does sleep with us at night, so even if the boa was left in there during the day, I'm sure my cat would go nuts with the boa moving around at night and stressing the snake out (not to mention keeping us from sleeping).

We should be buying a house in a few months, so at that point, I may be able to separate the snakes and the rats, but until then, I guess I'll have to see how things go.

I will be sure to be uber-careful about not handling the rats anytime close to when I handle the boa, washing my hands, etc. I am planning on hook training the boa anyway, so this may come in handy. I'm considering using the hook to transfer him to a smaller "travel" tub, putting the lid on it, then taking him out of the room to do any handling, that way he won't smell rats when he's being handled by me.

Thanks again for your advice.