If you're blistering the top, it sounds like you're probably heating it too fast and need to turn the heat down one way or another. How long are you heating it?
You should allow a few minutes per millimeter for the heat to soak through.
You can heat somewhat faster at the beginning, and then slower while the initial pulse of heat soaks though.
1/4" plastic is doable with single-sided heating.
Cycling the power on and off by hand does work.
You can cut the heat in half with an inexpensive heat control made from a big power diode (a.k.a. "rectifier"). Here's a thread about that over on www.tk560.com:
If you cut the power in half, you'll not only change the intensity of the IR, but the frequency distribution. That might actually be a good thing.
Doug Walsh designs his machines to run at an "efficient" element temperature (around 1350 or 1400 F IIRC) where the central hump of the IR emission distribution coincides with an IR absorption spectrum peak for most plastics.
(That is, the elements put out IR that plastics are especially good at absorbing.)
A different emission spectrum might work better, allowing more of the IR to penetrate further into the plastic, rather than burning the surface.
(A significant fraction can go right through, depending on the plastic, but with an aluminum reflector on the opposite side, you can get a double-sided heating effect to some extent. On a small top-heating machine, I've used an aluminum cookie sheet to bounce IR back up to/through clear acrylic. Seems to work fine; if the elements & plastic are pretty much surrounded by reflective walls, the IR will bounce around until most of it is absorbed by the plastic.)