"The problem is that it is warped at the bottom a good 2 inches."

Could you describe this warping in more detail? Or post a picture?
One of the problems with repairing old things is putting "heirloom" requirements on the repair... some old designs were prone to failure, but modern fixes clash with the value, or perceived value.
But I am sure there is a way to fix your problem; I just don't "see" it yet.

It is usually very difficult to unwarp wood. The reason for that is because wood has grain and if the wood warps, it is because the grain caused the movement. That means the wood is moving naturally and trying to force it against that movement is problematic.

Hi:
I had the same problem - warped about an inch - holding the door from closing tightly about half way up. I used a 1 inch wide flat steel bar (the door is about 1 1/16" thick). I spray painted to match, pre-drilled and countersank wood screws through the metal into the edge of the door. Worked perfectly - only thing, test first with the door closed to see if you need to plane a bit off the door's edge to accomodate the bar.
Good luck.....