I gather the moisture is immediately obvious to anyone that enters that room?

One consideration when using the sticky-edged products: if you have spills or moisture, it can degrade that adhesive and cause a failure or you can have adhesive seeping along the edges of each plank or tile.

Ha @Kristina Heimstaedt) and won't be damaged by moisture in the basement.

After investigating I found the moisture was coming from a HOLE in the tub !

I would be more concerned about the cause of mold given that it was newly renovated. you never know what's behind the drywall. basement moisture/leakage issue can cost a lot to fix especially it has been already finished. 

I've fixed flat roofs before that had moisture build up, but this roof had a hole in it.

With the water issues in your state you want a good grade flowing away from the house anyway to keep moisture at bay. 

Sand, stain and poly the existing wood floors (and obviously have something written into lease regarding protecting them within reason - keeping temperature and moisture regulated.)2. 

I just lost a shower/tub tiling due to cracks and moisture. ugh!  

The restoration companies have sensors that can detect hidden areas of moisture.