The moisture underneath caused it to rot and be invested with carpenter ants.

Pricing average vinyl laminate planks, durable, and waterproof (which costs more) at around ~$2.70/sq. ft; soundproofing moisture barrier underlayment at ~$.50/sq. ft.; and a labor cost of $2/sq. ft.

However, about 10 feet away, not near the laundry, I also noticed some moisture underneath some of the vinyl flooring.

If mold is on the joist that would be no problem to clean, just needs some equipment and on the sub floor i believe pending on how severe it is you may just get away with a cleaning with specialized chemical thats stronger than bleach (I know the name but cant remember how its spelled) , as well as a negative air machine, some duct tape, plastic sheething, tyvek suits, gloves and other ppe needed for the workers or it could be severe enough that the floors would have to come up (I know you dont like the sounds of that) and possibly trace it up the walls if any moisture wicked its way up sheetrock and the insulation thats in the walls?...

If the shower enclosure is in good shape and the remaining tile is just cosmetic pull it off, repair any drywall damage, and cover it with a shiplap or an accent wall panel (just make sure you use moisture-resistant materials). 

There place is musty and dank and probably some terrible moisture and water damage in the walls.

There was a gentle men that mentioned he had some that he knew in the Sacramento and Davis areas, and I am sorry I forgot his name, however these areas would work for us.  

If the area is not dry when the bleach evaporates, or moisture is still in the contaminated area (humidity, outside air dampness), you could re- start the contamination process immediately and to a greater degree.(9) Chlorine is a key component of DIOXIN.

These tenants will make their next move into an assisted living, some are very price sensitive, under market rent, and/or not really and truly able to fully care for themselves or their spaces and we generally try to gently nudge these tenants into more 'assisted' living situations be it with family or professionals.

Forced air is the way to go to prevent stagnant air build up and to prevent mold/moisture problems.