Upside down is the description we hear too often. You most certainly are not alone in this situation.
In your research you are discovering there are alternatives available such as a 'wrap around' mortgage. As others have noted, if you are too far under, there simply will not be sufficient market space to make this a feasible options. Great care must be taken to avoid the 'Due on Sale' clause included in nearly every mortgage that a 'wrap around' may trigger. The outcome of your loan modification may change your options significantly. Make certain you lender is advising you of the new refinancing options that are available also.
You do have options. However, each and every one must take into consideration your situation and the outcome that will be most beneficial to you. Your CPA, attorney and real estate adviser (a truly multi-dimensional one) can develop a proper plan with multiple exit strategies that will minimize your risk.
The hardest decision you must make is 'Do I need to keep my home?" Reconciling this reality is the most difficult. The rest is simply execution of the right strategy.
Reach out and talk to a few professionals. If they can not describe to you at least three strategies, then please keep looking. After all, one is short sale, two is 'wrap around' and how hard would it be to come up with just one more? Find the right professional, and take whatever action is needed to get on with your life.
Best of success to you.