Place the cup over your nose and mouth and breathe normally.

I predict you would have an easier time pulling out each of your toenails with an old rusted needle nose plier then to rent to this tenant.  

In the end we have bitten off our nose to spite our face.

Extremely unlikely to find acceptable tenants to live in those types of neighborhoods.I think you hit it on the nose with some of the neighborhood.

The general public is pretty unaware.If anyone in RE sticks their nose up at you, walk away, there are jerks in all walks of life.

In the basement I used my nose and sniffed along the wall - marked several areas and removed the drywall in those sections.

If they say yes then this is the case, if they say no, see below.Also, NO. 

The tenant just says that his doctor suggests there might be mold because the tenant has been experiencing cough, fatigue, headache, running nose, rash etc.... and they requested I get the house tested to prove no mold.

Don't run 1,000 miles away thinking the magic is "over there" when there are opportunities right under your nose.

In 6 months you could be at least out of the office.I'd say the best potential buyer is under your nose working with you.