Great answer Danny!
In addition to Danny's excellent response, I vacuum the cloth with a brush attachment before wiping it down. I have a central vacuum system that has a suction control valve on it to reduce suction ... preventing the unit from picking up the cloth. You can use a Shop Vac but if you can't reduce suction you will need to make an adapter using a piece of PVC pipe that you can drill a series of 1/4" holes, 4 - 6, and use tape over the holes to adjust the suction.
You want to pick up chalk dust not damage the cloth.
If you don't want to use the 10% - 90% mixture that Danny uses, a product called "Quick-Clean" is very good ... it's used at the US Open, Derby City Classic and the Men's Pro Tour. Dave Hodges also offers a washable micro - fiber pad that fits over a wide wand that makes it even easier to clean the cloth. Any damp spots with either method can be dried using a hair drier.
Polish the OB's
NOT the CB. Wipe the CB with micro-fiber towel often. Use a lighter CB e.g.: Red Circle or Measle Ball. The lighter ball will help with your draw, especially in your conditions.
IMO "Humidity" is the key. 72 degrees temperature & 72 degrees humidity is perfect for storing cigars
but 72 temp. & a lower humidity will go a long way to help with your problem. Even a few degrees can make a BIG difference. With your table in the basement, if you don't already have one, I would invest in a de-humidifier, By the way, my table is in my basement.
Proper environment along with & proper maintenance = Great Pool !