Unfortunately you like me are at their mercy. We pay our mortgage and bills. The only time your present bank will help you is if you don't pay them or give them all the paper work they will ask you for to show them that you are broke, which will take months.
Best bet is to refi with them or another lender, but most likely your upside down and your income may not meet their lending guidelines.
There is no fairness to those of us that pay and are border line for the new tougher lending requirements. Isn't unbelievable that the banks will tell you when you go to reduce your payments that you don't qualify for the amount your looking for. Just keep paying with those higher rates. Sort of an oxymorron.