The house seems to have wicked the moisture, so I think a dry out is necessary - fans and dehumidifiers.    

F and peak around 100-105 in the afternoon so it's boiled down to either remove the heat faster or slow down and/or stop the heat penetration but stopping the heat penetration is NOT attainable in my opinion and good luck if you wanna try.

If you go with the slightly under calc A/C unit, the compressor/condenser will run longer thus removing more moisture in your conditioned space.

It has been amazing & maintenance free.I recently went to a trade show & they had several booths with much the same product we used so its getting popular & some of them are now applied/sprayed on as a 2-3inch thick walk-on insulating foam impervious to moisture.

You pull down the ceilings in your unit, fill all the joist bays with mineral wool insulation, seal all floor penetrations with sound-proofing foam, and finally hang new drywall using resilient channel.

We've brought in two dehumidifiers which are helping, but I'm not sure what the root problem is or even who to ask for help.One contractor said moisture is coming through a hole in the exterior stucco, but another said no way because the vapor barrier would block it. 1st one recommended installing insulation, but I've also read this can increase condensation problems.

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will take care of the premises, keeping them clean and clear of debris.

Dry all studs and sheathing to 12% moisture (some contractor’s use 15%).

Here is the link:https://www.epa.gov/mold/printable-version-brief-g...It's a good read, whether or not there is the potential for lead based paint to be disturbed.Another booklet about "Mold, Moisture and Your Home" is also an essential communication that every landlord should be giving to every tenant.

If the existing floor is vinyl, the answer should be yes, you can because vinyl provides a good moisture seal.