Well, if your home were completely paid off, and had no first mortgage or lien on it, you might want to consider possibly owner financing. Owner financing, would allow you to still do a background or credit on the buyers, and charge interest to the buyers, just like your mortgage charges you. There are many pro's and con's regarding owner financing....so be sure and speak with your attorney or Realtor. In some states such as ours, the title actually changes hands and a deed of trust is made, other states can differ drastically. If, this doesn't work for you, try and look for a foreclosure or distressed, or motivated owner in the area you want to move to, that might accept a lower priced offer from you. However, until the market values in your area, return to normal, your loss, is probably still a loss. I am not quite sure why you would want to borrow to cover a loss, and rolling it into another mortgage, just puts more interest on top of it, possibly resulting in negative amortization.
Speak with a good Realtor, and let them run some comps for you to actually ascertain what your market price might be, or possibly suggest a good appraiser. Maybe, hopefully, your home has something the others don't and your value turns out to be better than you think it is. Good luck!