I haven't been able to resolve our issues here either, but we on occasion once a tenant leaves is to pull off the register, scrape the texture, spray a 10-1 ratio bleach and water on the affected area, let dry and get a can of spray texture and then touch-up paint. 

Check the place out, clean up, lift necessary flooring, bleach any stain on the sub floor, paint with kilz and reinstall flooring or replace.

bleach

Re-doing kitchens and baths makes the potential buyer feel like they are purchasing the rehab from you at a cost, show old appliances that are bleached and do not smell.

Get a gallon sprayer, fill it halfway up, and dump two cups of concentrated household bleach on it.

Bleach and large fans 

He verified that it wasn't from a pipe, but told the tenant to just use a little bit of bleach and water to clean up the mold (ughhhhh, i really wanted him to clean it up, but what am i going to do).  

(Dadumdumdumdumdum)1)  Get a 1-3 gallon pump sprayer.2)  Fill it with bleach3)  Add one bottle of dawn dish detergent.When you pump the spray on the beams, the bleach kills the mold and the dish detergent holds it to the beam till the job is done.This is what FEMA prescribes, it does work, and best of all, it's cheap!!

If you want smooth, it might call for actually removing stucco and putting new one, it will not be cheap, if you want cheap, power wash with bleach or tsp, scratch and overlap but frames will always be an issue. this overlap might need about 1/2" more, so not that bad.

Cleant he wook with 50% water 50% bleach.