I have been playing with this for a while. Best thing I have found is a heavy piece of steel. Works on softballs too which is a lot more stubborn. I use a piece that weighs about 30lbs. They were some scraps I found at the steel yard, about an inch thick. But I have noticed once flattened out if left unchecked it will get some of the cup back in. When I glue these together, I slather a good coat of weldwood on both sides, stitch about half way around and stick under the plate before the glue has a chance to set. I leave it alone overnight. Even after all that, a very little cup or twist is not uncommon when all is said and done. If you can come up with a design to cut some I've the cup out of the leather it will help quite a bit.
Side note, the cover on baseballs is real leather, the cover on softballs is thinner than the leather used on big box store wallets, glued on some kind of backer.
http://tntanningcompany.com/index.html
this is the company that makes the leather for the balls used by Major League Baseball. It is a company owned by Rawlings. I think they sell baseball leather. I called to ask, another guy was supposed to call me back and never did and I never followed up.