Hot hairdryer and then books?
I think you need something with heat, because the heat of the dishwashing was what probably made them curl to begin with.

What if you heated them up first and then tried to flatten them? Or maybe take them out of the dishwasher during the heated dry cycle, while they're really warm, and then put cookbooks on them and then sit on top of the cookbooks for awhile.

My suggestion is to buy a few more from Ikea. They come two to a package, and a package costs something like $2.

Are they the IKEA ones? I rebend mine by interrupting the dry cycle of the dishwasher halfway through, pulling out the cutting boards (they will be hot and damp) and then stacking books on top.

They're curling, huh? Think of it as a feature: this makes it easier to scrape chopped things into a smaller thing like a pan or a tupperware.

It is NOT a feature. It makes it very difficult to cut to have to hold down the board with one hand, and is probably dangerous. They're designed to be flexible--that is a feature, but being permanently stuck in a curve is not.

Mayhap roll them up like a poster in the opposite direction, then run them through the dishwasher?

Place cutting boards in sink. Fill sink with hot water (heat water in microwave if your hot water heater won't get the water scalding hot). Place bricks (or rocks, or whatever you have that's heavy and waterproof) on cutting boards' curled edges. Sit down, open beer, watch TV until they've cooled. Ta-da!

I've done this with disc golf frisbees that I've warped by bouncing them off trees, and it works like a charm.