I've been looking at portable dehumidifiers for a quick solution to the humidity problems. They seem to be divided into ones that are quiet and the fan runs all the time, whether it's dehumidifying or not (like Soleus, Danby) and ones that are noisy but the fan doesn't run all the time, like GE.
apparently when people have a dehumidifier in their living space they want the fan to run all the time, it's less disturbing than having it turn on and off. I'm not sure I'd feel that way - so, I figure one could get a quiet one, set it so it's continuously dehumidifying, but put its power source in series with a separate dehumidistat.
Most of the dehumidistats are meant to be wall mounted and wired to the house power. Probably my helpful local electric supply store can help me convert one of those to something that plugs into the wall and has a receptacle for the dehumidifier plug.
There are plug-in dehumidistats, Dayton 1UHG2 and Honeywell H46E. The Dayton one has a +/-1 range for RH, the Honeywell has a 5% range. The 5% range would be better so it doesn't cycle on and off a lot.