You might try Boric acid powder for the bugs, run it along the perimeters of baseboards, cabinet, shelves, etc. They'll eventually carry it into those places they hid and kill others with it, though the humidity might shorten it's effective life.
Less 'toxic is old fashioned fly paper or card and paper treated with "tangle-foot" http://www.tanglefoot.com/products/ttcoating.htm tacked to the baseboards, etc as well as corners of walls/celling 'V' fashioned where they might also snag their share, especially if you bait it with attractor from 'roach-motels'. Tack/ wrap bands of this sticky stuff to the legs of tables, sinks etc.
Or you could try keeping several small, insect eating pet lizards in the room when not in use.
The most important thing is getting rid of sources of standing water, including from print washers and blocking drains with tight screens at a minimum. As I understand it, Roaches must have a source of water to thrive and though you can't do anything about the rain, you can do things like filling in pot holes underneath the house, if in one, keeping potted-plant dishes free of standing water by using cloth 'wicks' in the basins, not allowing Damp-Rid collectors to stand with collected water exposed, etc.
Air conditioning or heating are the only ways I know to remove the moisture but be careful if you use boric acid, not to raise it up to be breath in, by-way-of excess air currents.
I hope this helps, good luck,