I did some calculations based on vague guesses about the steel. In theory, I'd need to bend the plate at least 1/8" in the middle to reach the yield point where it wouldn't just spring back, and it would take ~400 pounds of force to flex it that much. Certainly more than I could do by jumping up & down on it.
I talked to the head of the machine shop at work, and he volunteered to help me flatten it out using a giant DiAcro hydraulic press brake they have. The key feature is that you can control the depth of the stroke in1 thousandths of an inch. I brought the plate in at lunch, helped him remove the dies off the brake and then set the plate up on a couple of aluminum bars supporting the ends. To push down in the middle, I had a chunk of 2x3 wood set on edge, and a piece of plywood to spread the force out over about a 3" wide stripe.
We started slowly increasing the depth of the stroke in 20 thousandths increments, watching the plate flex more and more. After each stroke, we'd check it with a straight-edge for any signs of flattening. It just acted like a giant leaf spring, well past the 1/8" depth I'd calculated. Even at about 1/2" deflection, there was no obvious sign of progress. Finally, it began to flatten out. It eventually began to develop a shallow depression in the middle where we were pushing, but by then the overall curvature was down to only 10 thousandths or so. The remaining upward curve was a bit off-center at that point, so we kept the stroke the same and moved the wood off a bit to that side. At the end, the final stroke was just about 0.800"! We were getting very concerned that the end blocks were going to kick out from under the plate because the angle was getting a bit steep. I have no idea how many pounds it took to bend the plate that far, but it was a LOT.
When finished, the overall flatness is probably down to about 5 thousandths, and it's in places where it should flatten out even further when it gets bolted back down to the press. Needless to say, I'm very pleased with the results. There is no other way I would have been able to do this without driving over it with a car, and the lack of control would have made it a very haphazard process. As it was, it took us over3/4 of an hour carefully flexing & checking things.
Flexing a piece of 1/4" thick steel 8 tenths of an inch is an amazing sight. The only guess we have about how it got that warped in the first place is stresses that relaxed over time. There is no way that much force could have been applied to it while it was on the shear without something else suffering damage. The press is probably 40 years old or so, and there is no sign it was ever in a fire that could have warped it like that.
The only other note is that it was kind of nice using the big DiAcro press to restore my little DiAcro shear. Sort of keeps it all in the family...