Put the home on the market and allow the market to work. If the person you are talking about is willing to offer more than anyone else, disclose, disclose, disclose and have your agent submit the offer.
I would want your home to be on the market at least close to the average number of days for your area at a reasonable price before I would submit the offer.
Everything must be above board and if other legitimate offers come in, they should also be disclosed to the bank. I can't guarantee this will work, but if everything is done transparently and your shoestring relative is willing to pay the most, they shouldn't be excluded.
A short sale should be an "arms length" transaction and many lenders will require you and the buyer and both realtors to sign an affidavit before a notary that the person buying your house via short sale has no personal or business relationship with you.
If you're not planning on living there, why take the chance that you can be found in short sale fraud by selling to an family member?
Good luck and best to just sell it on the open market for the highest possible price so you cannot be accused of engaging in fraud.