So what we do is remove the ac unit, furnace, a-coil and water tank.

But if you talk to your building inspector and let him or her know what you are doing, it probably wont.)If you are replacing windows, you should be sure to either put aluminum coil stock around the exterior trim or wet scrape and repaint the exterior trim. 

I'd also get an estimate for ripping out all the carpet, flooring, cleaning the AC ducts, cleaning the inside coil and doing a complete paint job. 

TN, CO, IL, IA, WI, etc etc. 

Because it isn't WA, OR, CA, CO, Il, NY or other places that despise investors and hate cops.

Randy  I agree that a starting capacitor is a very common problem.Sometimes they coolant gets low from a small leak and causes the coil to freeze over.If it's a split unit I would see if the pipe that has the insulation on it from the outdoor unit is cold or cool.Also see if the outdoor fan is turning.

Or, in the alternative, some guy on Youtube used 400 grit sandpaper to clean his all nice and shiny, but I'm wondering if the abrasion would short the coil?

You might be able to get by with replacing the evaporator coil and a blower if the system isn’t that old.

On one of the rentals, I had an HVAC replacement expense of $2800 for a coil.

If much of the basic basement finishing happened way back when, you probably have, behind the walls, plastic sheeting stretched across the concrete block walls, fiberglass batts stuffed into the rim joist cavities, organic fiberboard insulation lining the plastic, and regular drywall with untreated 2x2's serving as studs, nailed into the concrete masonry block walls with a powder-actuated nailer.