Any thoughts about the diatomaceous earth? I've read that it's quite safe as long as one doesn't breathe it, and that it's fairly effective in low humidity environments. Do you have any experience with the stuff?

If you think about the rate of cockroach reproduction, you will probably decide trapping is hopeless. If you feed them, they will keep ahead of any trapping or killing approaches. My wife suggests changing your paradigm. Think of the cockroaches as pets. You are feeding them and providing a happy home for them. If you don't like them as pets, stop feeding them.
Rick

"Since moving to Florida, our home has been infested with roaches. There is an old remedy that the Japanese people use. that includes white flour, boric acid, and powdered sugar.

Mix equal amounts of boraci acid and flour. Then add just enough confectioners sugar to attract the roaches. Add just enough water to make a soft dough. Roll the dough into little balls and place in the little candy paper cups (like the cups muffins come in). Place the balls in corners of cupboards and behind fruniture where other animal life cannot reach. The roaches eat this and it causes them to dry out. It takes about two to three weeks before they will be completely gone. Replace the boric acid balls every month to ensure that there is no reinfestation."

Roaches like masking tape glue. Take the masking tape and line the edge of a door jamb with it so that half of the tape is sticking outward. The cockroaches are attracted to the glue, climb onto the tape and start eating the glue, but they get stuck in the process. Result: roach strips.
Works very well.
Jeff Prill

Slight modification to this method:

Get Boric Acid CRYSTALS and dissolve them in water, an ounce or so to a quart. Use CRYSTALS because the POWDER is very hard to dissolve. Fill up a sprayer and spray EVERYWHERE. Spraying also allows you to get into places that you cannot otherwise get into, like cracks, around pipe-holes, etc. When the solution evaporates, you are left with a very fine layer of Boric Acid all over everything. A little goes a long way.

I forget the actual chemistry around this, but it boils down to something like this: The Boric Acid has no odor, so the roaches do not avoid it. They (the roaches) are naturally "clean" insects that constantly groom themselves. The Boric Acid gets into their systems and "eats" them from the inside. They do not develop immunity to it and never "learn" to avoid it (both traits with normal poisons), so it keeps on working. On a positive side, Boric Acid is relatively non-harmful to anything else that might exist in the area, such as cats, dogs, and children.

Joe.
My opinions only, your mileage will vary.