Well, I said I'd try some things and report my findings, so here they are. The best results I got didn't take long at all. What you'll need to do what I did is a steam iron & ironing board; a nice, thick 100% cotten bath towel; some paper towels; something heavy and flat that's larger than 10" in diameter (like a stack of 12" 78's, but make sure they're not even SLIGHTLY warped); and a large, flat stationery surface that's fairly rigid and smooth (like a small stack of 12" 78's that are, again, perfectly flat).
Wash your hands thoroughly before handling any of the items. First, prepare the second phase of flattening by making your flattening sandwich ready and easy to put together quickly; if you're using 12" 78's, for instance, place a stack of 3 next to a stack of 10 on a table near the ironing board, with a paper towel (large enough to cover the entire disc surface) on top of each stack. Fill the iron with distilled water and set it to decently high temperature, enough for it to steam easily. Put the HOTW disc playing surface down on the ironing board (feel around for a spot that's flat and free of too many projectile things going on underneath the board pad). Fold the bath towel in half and cover the HOTW completely (this is actually tricky with the more stubborn and severely curved discs, but be patient and don't be afraid to manhandle things a bit if necessary). Hold the iron over the towel/disc/ironing board horizontally so that it steams, and push the steam button repeatedly if your iron has one. Lower the iron to an inch above the towel and distrubute a good amount of steam evenly over the disc area, dampening the top layer of the towel substantially. After a minute or so of this, press the iron down and iron the towel flat, moving in circles around the disc area. Do this for 45 seconds to 1 minute, occasionally hovering the iron above the surface to facilitate more steam. In a fairly quick motion, place the iron safely aside and slide the disc out from under the bath towel. It will not be playably flat just yet. Place the disc on top of the paper towel that's on the stack of 3 12" 78's, then cover the disc with the 2nd paper towel and gently place the stack of 10 on top. Leave it there for a couple of minutes. Then remove the stack of 10 and the top paper towel, and place the disc on your turntable as if you're ready to play it. Over the next 5 to 10 minutes, it will continue to settle down into a flat shape until it should be quite playable. The last phase really caught me by surprise... I had used too much steam on one disc and it bowed the other way after having been in the flattening sandwich, and it wouldn't play. I was going to give it another shot and leave it in the sandwich for an hour this time, but I got a phone call that lasted about 7 minutes. By the time I went to take the disc from the turntable for round 2, I noticed it was visibly flatter than before, and it played just fine when I tried again to play it. Absolutely no treble was reduced, not even on the longer-playing HOTW's, and no sonic degradations resulted. The grooves of some discs did take on a very subtle elliptical shape, but this caused no pitch fluctuations whatsoever, and I'm not positive they weren't already that way from whatever curled the discs in the first place. Best, Robert