The PL adhesive is plenty strong for the application at hand. You'll be fine. It wouldn't have mattered if you had used a resin type of adhesive with 100% coverage, the panel would still warp unless it is balanced.
You say you currently have it clamped flat. I would recommend clamping it past flat and putting an opposite bow in it about double the amount of the initial bow. For example, if you could take a straight edge from top to bottom on your door and there was a half inch gap in the middle, then lay your door upside down on a long work bench, place a 1" shim in the middle, and then clamp the ends down.