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I can't address Chess Pie specifically (not my tradition and never ventured into even trying one), but I can address custard. They always sink/deflate, but especially if overcooked. Just yesterday I made a custard tart that went from almost 2 inches of liquid custard to about 1.5 inches cooked and yummy custard. And this one (new recipe to me) had the egg white whipped and folded into the custard mix. I thought that might reduce shrinkage but what it did was create a foamy cap on the tart... which was nice but not necessary.
p.s. No milk cream in the recipe? How does the custard form in a Chess Pie?
I think you missed my point. Your recipe is not a typical custard pie and seems to not be forming a custard because of that fact. Custard = egg + dairy... usually 2 egg per cup of dairy at a minimum. You have no dairy in your recipe. I've never seen a chess pie recipe without at least some dairy in it. All "traditional" custard pies have more dairy in them.