About the flat raised area - and holding it flat while bashing out the rest of it .....
I would cut some 3/4in plywood to fit in the recess side - good one-side stuff (not the
Crap
Doo
Xcrement)
And then stack another twin of that up on top with a big heavy weight on it, to pin the panel to the bench - while working out the crash hash all around it.
May need to elevate the stack up off the bench to get hand and dolly underneath.
Then slap and straighten and shrink around the perimeter area, using the workbench as a depth/height guide.
Go back and tune up the center a bit now and then - don't go overboard on THAT. It will come along as the perimeter comes around.
Good luck, and write back as the scenery improves.
(Warning: overdoing shrinking on flat thin areas can be detrimental to your joy and patience.)
(Oil cans happen. Get used to them.)