I would do exactly what I am doing, I am holding all of my properties, I have not sold a single one in over a year. Other then a vacent lot, but I got full asking price.
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Let’s be realistic, it’s the price and condition that matter to buyers. There are so few of them today, that you have to practically give it away. So what if you have to pay a few thousand dollars at closing, reduce the price and make it sell! OR sell on a contract for deed. OR Rent it out. You have some choices. But do not think that walking away from it will solve your problem, it will in fact create a whole host of other issues that will follow you for up to 10 years. Example; a foreclosure impacts your whole financial picture, from getting jobs, to your credit cards. I know from experience.

You need to think outside the box and do whatever is necessary to accommodate your move and not ruin your credit.
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How much do you own versus how much do you owe? If there is enough equity to pay off the bank or close to it, you can short sell. many banks will settle for a high percentage of the loan and let you off the hook. In these times, they would rather do that then foreclose because they would then owe the taxes. Foreclosure means ownership change. Short sale means you own it until it sells and the bank agrees to take less than the full amount of the mortgage.

Will the bank let you off the hook? Sometimes the bank will hard-nose and if you have a good job, they will sue for the balance due after they foreclose. You could end up without the house and with a debt that would stop you from getting a new loan.

Before you do anything, consult a lawyer. The few hundred dollars he will charge will be well worth it. He may even be able to negotiate with the bank.
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