So are you still having problems with the humidity?
You are right with the dew point situation btw. When the wet-bulb temp reaches the same as the dry bulb, then you get condensation.
You might have a problem with sealing the unit due to the fact that the cooling section runs so long for so many times in a day. The longer it runs, the more moisture it removes, obviously, but if the temp. control is f-d, it could be running way too long. Plugging that drain, and any other problematic opening to outside, would be the best thing to do right off the hop.
Thermo-electric units should technically be a lot better for condensation problems than units that move air, you should not be having that much of a problem in there.
How about an update to let us know how you are doing.