Take a look at this link. http://www.homedepot.com/p/DRIcore-7-8-in-x-2-ft-x...You can also install a vapor barrier to prevent cold air, moisture, etc from coming up through.

You have to regularly inspect it.You might have a moisture problem.

You may see this moisture escape in brick that has white streaks or areas known as efflorescence.

So, you could be developing moisture damage in a major way.

Applying the wet drywall mud to the clean may loosen the popcorn texture due to adding moisture to the product. 

I've listed below the order I plan to attack things in, let me know if this sequence makes sense:Resolve excess moisture under house (minor grading issue, gutter required, possible plumbing leak)Repair minor roof leaks (repair flashing, seal leaks around chimney, replace tree-damaged shingles)Trim trees away from houseInstall 50 concrete piers and level foundation (foundation had work done previously but shifter due to excess moisture)Install vapor barrierAdd structural roof support beams in attic, add insulationRepair rotten siding/soffit/window frames (mostly upstairs)Repair porch (replace rotten boards, sand & paint)Paint exteriorInstall central AC/Mini-split system (any recommendations on this?)

Or that their insulation hasn't been upgraded in 20 years and the kitchen vent is venting moisture into the attic causing higher electrical bills...

Water is getting in somehow and has to be stopped or moisture will just come back again.As a landlord you are not a mold expert.

I would definately do a home and moisture termite inspection.  

Moisture meter only showed right in that immediate area.