If you can't put a monitoring valve on the water supply can you put a water moisture alarms somewhere below her?  

I Think Drywall on basement ceilings is a bad idea, in all my houses it inhibits getting to too much of the plumbing and electrical.I always update ceiling fans, they are cheap and a good new one is a better investment that having potential complains about the old one if it were to fail.What does the wood paneling look like, newer stuff is difficult to paint, while older paneling may have moisture problems and need to be removed.

SOMETIMES the problem is caused by the idiot who decided to put vinyl on OVER THE TOP of the old, maybe faux board siding.If there was moisture in the old siding it's going to manifest itself by creating condensation on the outside.

Check with a moisture meter.  

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.

Either a dry-lok type product if moisture is an issue or regular paint suitable for concrete.The flooring is something I am running into problems with.  

Much cheaper than a chimney cap that still allows moisture & wind infiltration.

Open cracks plus a humid climate that gets heavy bouts of rain creates all kinds of problems from moisture intrusion.

The glue was good, but it didn't solve all moisture problems.

We also detected moisture using the inspectors device in one of the walls, but did not see any water in the basement.