I covered the visible screws with spackling paste and sanded the frame, then applied two coats of Behr Ultra black eggshell primer and paint.
Masking and painting the bottom lip of the frame. Overkill? Absolutely.
Frame painted. Here, I’m using stir sticks to visualize how much higher the ‘ground’ should be.
After the paint was dry, I sealed the entire project (top, sides, and bottom) with two coats of Zinsser Bull’s Eye shellac. That should help to mitigate some shrinking and warping. (Note: I sprayed the shellac outdoors. This photo was taken several hours later, after it had dried.)