I agree, if the original deal was breached, you could say "well then, I want joint physical custody".
In my state, if you have joint physical custody 50:50, there usually is no child support paid, I believe.
(Not that I like that idea - usually there is one parent who has more of a burden to provide home etc and makes sense for them to receive some support for that.)
Be careful, though, about how you look at things. $28,000 sounds like a lot. $200 more a month may be entirely reasonable, depending on circumstances. Don't horribilize.
What confuses me about your situation is, usually child support is figured according to a formula. A formula, btw, that often seems pretty fair, when you consider the costs involved in providing a home and raising kids. What does the formula in your state say she should get? Courts often don't like to let people trade away their child support, so if you're currently paying a lot less than your support should be, the courts would probably side with her.
The sad truth is, kids are expensive, and it's much more expensive to maintain two households than one - everybody has to take a cut in standard of living.
And how are you ending up with all of the debt? If she wants child support according to the formula then shouldn't debt and assets be split 50:50?