What could I have done to prevent crust pieces from submerging themselves in the filling?

Hi Randi-- eek! Been there. I will look into a longterm solution, but when this happens to me, I bake the custard/pie until it begins to set, and then add my pie dough pieces, which I have brushed with eggwash and a little extra sugar in advance. Hopefully with the addition of the sugar, and perhaps set on the top rack of the oven, the pie dough still browns to your liking for crispy, flaky, deliciousness.