Whoever told you to short sell your house needs to get educated. They are basically a last option before going into foreclosure. Your situation doesn't seem to require that at all (correct me if I am wrong). Short selling your house is basically when the bank says you cannot pay and decides to sell because their losses would be less - without going through the extra fees and time of the foreclosure process.
With the whole relocation thing. Like Richie said, usually the employer has a process to help you in selling your home for fair market value and it's taken care of.
I'm not sure why mortgage modification came up because it seems like you just want to move (not sure if it's an upgrade or downgrade).
From the sound of it, you just want to sell your house to get into your next one. If this is the case, you have to be cognizant of the current real estate market. Quite frankly it's crap right now and banks are extremely stringent on new loans so you don't want to hurt your credit. If you found your dream home and are scared of losing it, you may have to just lower your price and just get more aggressive about selling it. If you have the time... don't kill yourself.