I agree central a/c is the way to go.But you will need the a/c condenser, a pad (or suspend it on brackets), evap coil, line set, electrical circuit & disconnect so you're probably looking at closer to $2500-$3000  using compatible Goodman parts & depending on what they charge to install it, (usually around $800-$1000).

Not sure how you clean something for a smell... but can imagine that they might also do things where the unit was just dirty... like clean the coils, etc that may not be applicable to a smell... so you might be able to argue that some of his maintenance was preventative, and not tenant induced.  

Location - Spring, TXBuilt in 1977, 3/2, approx 1500 sqftContract Price - $120kLocked-in Mortgage Rate - 3.5%Total Monthly Rent - $1450- Comes with Section 8 Tenant (Mom & 3 kids)- Buyer pays title insurance- Big items to account for after inspection: Tree too close to the house, needs to be cut downOne side of the garage door opener has no outlet to plug into (there are a total of 2 single garage doors)Kitchen sink drain pipes are "amateurishly" doneRusting of the evaporator coil in the attic (20 yrs old)Attic lines don't have enough insulationOne bathroom toilet is cracking and needs to be securedRoof is missing guttersRoof shingles vs flashing wasn't done 100% correct, needs more spaceThe buyer agreed to a $500 closing cost credit.

Location - Spring, TXBuilt in 1977, 3/2, approx 1500 sqftContract Price - $120kLocked-in Mortgage Rate - 3.5%, 20% down (no points)Total Monthly Rent - $1450- Comes with Section 8 Tenant (Mom & 3 kids)- Buyer pays title insurance- Big items to account for after inspection (Est $2-2.5k for bare minimum): Tree too close to the house, needs to be cut downOne side of the garage door opener has no outlet to plug into (there are a total of 2 single garage doors)Kitchen sink drain pipes are "amateurishly" doneRusting of the evaporator coil in the attic (20 yrs old)Attic lines don't have enough insulationOne bathroom toilet is cracking and needs to be securedRoof is missing guttersRoof shingles vs flashing wasn't done 100% correct, needs more spaceThe buyer agreed to a $500 closing cost credit.

When I sold the building I had the coils cleaned.

I have not tried this but an HVAC company suggested UV lights installed in the ductwork or near the AC coil, but I also see stand alone ultraviolet air purifier by googling. 

The compressor is shot so the bulk of the price is a new part, then some smaller valve replacements and new coolant for the coils.

I would be shocked if a unit could run efficiently, or even at all, after three years of return air passing over the coils without a filter.

If there is a leak in the coil, I think it was about $600 to replace. 4.

Whether it be a coil in the boiler or an indirect water heater.