I have moved a couple of bowed fronts back in, but can't be exact as to how much travel there was as I never put a tape to any of them. I use a couple of 36inch bar/spread clamps (or whatever you call them.) Put a strip of 1x2 along the front lip and one along the back to distribute the pressure. Strips should be about 1/3 the length of the cookbox. Reason for this is that while you want to distribute the force a bit, you still only want the middle to move. Might not be necessary, but that's the way I've been doing it. Anyways, put the boards in place, put the clamps in position and tighten then down til snug. Then crank them just a little bit more. Give it some time, then crank down even more. At some point, you need to get it to where the front lip actually bows inward just a bit. Leave it there for a day or two. When you remove the clamps, it will move back out a bit, but hopefully it will be closer to true.
Just an FYI, I don't know if all these steps are necessary. That's just the way I've figured out to do it.