Sadly, it is not flat. It has a slight cup. I had been hoping that by buying 1/2" thick material, that it would be reasonably flat, but no such luck. Since I don't have a torch, I don't really think that I have a way of straightening it either. So I welded it on with four, about 1" long welds, at the corners, and if the time comes that I decide to straighten it, it will be relatively easy to remove, but for now, I'm just going to leave it as-is and suck it up.
I considered for a moment running beads along the back side, but I decided not to for two reasons: first, I think that heat might be too localized for the gradual curve that the piece has, and second, it would leave a bunch of weld metal on the back side that I would have to grind off. I think a rosebud tip on an O/A or Oxy-Propane torch would be the right tool, and I don't have one. Maybe if I was more motivated, I could transport the top to a machine shop and get them to straighten it for me.