In fact even when you hear yes the terms that usually follow are so bad you are going to say no!

You don't want to be buying in a market that you have no clue what the good and bad areas are.

The concrete steps at my rental property have had a bad winter.

@Kris Benson is correct. 7 square feet per person is considered the industry standard for market equilibrium, less than that, the market is considered under supplied (good), more than that, the market is considered over supplied (bad).

Now that might not be a bad thing if I made enough so that I owed more than $7,683 in taxes this year, because it would just even out later.  

Too bad but that's the way it's currently set up and I don't see anything to indicate that that will change.

It's an SFR, roughly 100 years old, with a foundation that is in bad shape.

So selling and requiring a contingency with a floating closing date for you to find your replacement is not a bad thing to explore at all. 

@Anh Le Doing a 1031 exchange to avoid capital gains taxes might not be a bad idea for you in this situation.

It could be low on reserves, credit rating, consumer debt, income- good or bad in any category they will tell you what they need to see.