Thank you for sharing your dilemma. I can't imagine how hard it must be with two great schools and so much money being thrown at you :P
I am going with the assumption that your T15 school is either Stern or Johnson, because of what you mentioned about IB. I would not worry about the reneging. Your career is more important than a weird binding decision that (in my opinion) chokes people.
There is ZERO downside in asking for more aid. What do you have to be ungrateful about? You did very well in your application and that's why CBS admitted you. Asking them to make the decision a bit easier is NOT a bad call. Whether you want to mention your other admit is a separate issue and we can chat about that, but I would not worry about saying no to them.
It looks like you can achieve your goals realistically with either schools, so in that case the CBS brand would not perhaps matter all that much. However, if this was Duke or McCombs(which is not that great for IB to be honest), I'd be more inclined with going to CBS with $0.