Thanks for all the great suggestions on fixing the playfield. Here is what I have tried in the past and also what I did this time.
Try #1. On another Allwin, I completely removed the playfield from the game and tried to evenly heat the entire thing with a heat gun. I thought that if I got the entire thing to the same magic temperature it would just flatten all on its own like a good little play field. It didn't and I wound up melting one corner.
Try #2. I decided it needed some weight on top while I was heating it. I placed a large sheet of glass on top of the play field and some heavy weights on top of the glass. I then heated the glass for a long time with the heat gun. Not enough heat was getting to the playfield and eventually the glass shattered.
This time #1. I decided to try flattening the playfield in the game. I removed the 12 winning hole thingie. Just 4 screws on the back so that was easy. There were 4 tiny nails in the plastic just above the holes. They took a while to get out because I didn't want to crack the plastic were they were driven in. Then I took out my heat gun, set it on low, and heated one small section for about 30 seconds. No change so I touched it to see if it was hot enough. It was and have the burnt finger tip to prove it.
I decided I needed to protect my little paw so I got out the old family asbestos gloves. If you don't have a pair of asbestos gloves sitting around an oven mitten will work. Just don't use the one with old food stuck to it.
This time #2. I applied heat to the playfield, one small section at a time. Then stopped the heat and I rubbed it (with my gloved hand), pressed it flat, held it as it cooled and told it that it was pretty pretty playfield. I kept repeating that over all the bad spots. It only took about 15 minutes and it was flat enough to work again.
I had to trim the plastic a little around the slot where the 12 winning hole thingie goes. I also didn't put the 4 tiny nails back in. They were a big part of the reason the play field buckled.
I don't know how well you can see it in the earlier picture but the playfield was buckled all the way across the top of the winning holes and it was impossible to get the ball in any hole.
The playfield isn't perfect but game plays great now and that is all that really matters.
Thanks again for all your help.