The whites just get destroyed faster even with bleach and hydrogen peroxide treatments. 

Dude just one point that mold is nothing its so common and the inspectors use this to scare you which they have done.. a little bleach spray it on wipe it off boom its gone..

They can be bleached to get most small stains out fairly easily.  

Just look at how people went crazy over grocery store items during Covid - not limited to toilet paper and bleach.

I pointed this out and their response was that it "looked bleached" and "showed that chemicals were used" once under a blacklight...

I had a remediation contractor come out, and he told me the levels on the report is what he'd expect from a basement in Portland, and any amount of washing / bleaching wouldn't reduce the levels much long term as more moisture would enter the space up from the slab because concrete will always give off some moisture, and he couldn't really recommend much remediation. 

I believe this can be taken care of with bleach and a power washer.  

Many of the homes I´ve acquired took weeks of bleach, ammonia, pinesol and scrubbing to get the stink out.

I'm not that professional but I think a whole house filter would filter particulates like dirt but not chlorine. for chlorine you might need a reverse osmosis system for a specific drinking water tap to eliminate the taste as it's not practical or efficient to put an RO on the whole house supply. if skin issues from bathing are a problem you might need a softener. sometimes when kids have eczema doctors actually prescribe "bleach baths" where a small amount of chlorine bleach is added to the bath water. also many of the water treatment systems can be rented so maybe just rent it while they are there. regardless, proceed with data. water test, pediatrician diagnosis (if it's legal to ask for, no clue), and a system that is right for the application. sounds like the tenant is willing to help out which is awesome.

., bleach, ammonia, popular cleaning solutions "guaranteed" to sanitize etc.) spread on Agar plates that were then incubated in a warmer.