Like everyone else, I am not 100% sure how this plays out.

The bonus on this is it doesn't show up on your credit report either. 

After standard deduction 24,800(married filing jointly), I have a negative taxable income of -24800 which is same as 0, meaning I don't get any bonus points for having large negative income.

I do understand size plays a part in this so let's say a house is 1500sf.

You are losing $70/month on the mortgage alone, and without knowing what else your "payment" figure includes, it could be hundreds more in PM fees, property taxes, insurance, maintenance, etc.The refi certainly seems more appealing at a glance but again, if we have to consider the additional expenses listed above you'll still end up underwater.Honestly, it seems like unloading this thing any way you can in order to limit your losses seems like the best play.

I'm thinking of ways to speed the process up, like offering a gift card as a leasing bonus.

Maybe a section 8 play could work. 

I know it's kind of backwards to invest in properties than further down the line "house hack" but that's just how circumstances played out for me with my current home. 

Neither party has to play games with the other.

@George ChungDepends on number of factors such as how good are your financial records (balance sheet, income statement), how many state returns there are, just to name a couple of the factors in play.