Is there room for negotiation or compromise?

And any amount you purchase over the amount of your sale adds depreciable basis to your property and does create more depreciation allowance.Your situation isn't hopeless but it's probably going to have to be multi faceted and one where you have to compromise a little.Unless you simply do a cash out refinance and let the property support the new debt. 

It was a brand new countertop before they moved in and I don't want to settle for just a repair if it could possibly lead to compromising the countertop down the road.

I came here because the arts world is full of compromise and sacrifice- body, spirit, finances, time, and most importantly, family.

Personally I would not send a letter or an email .i would drive right over there immediately walk rIght up to the door and tell the idiot to hIs face to lose the dog or he will be evicted then I’d hand him the quit or pay notice right then and tell him to improve his conduct or him and Fido will be whimperIng on the street . ..or you could kindly send him an email bake him some fresh sugar cookies and ask him if he was willing to compromise with just 3 pit bulls in the house

Does anyone know of a way to do this without compromising the mortgage process?

I think there will be compromise, depending on what you're open to and where you can be flexible.I like Scott's advice though on starting with local banks to you. 

Compromise requires each party to get something of value, not just something that you consider of value.

He is willing to compromise on an sell price way below of 350-375K..

Originally posted by @Isiah Ferguson:...A nice compromise I suppose.