I'd use an oil/floor dry product (clay or diatomaceous earth) for a day or two. Standard cat litter would also work in a pinch. This should pull most of it out.
You'll want to prime the raw wood anyway, so use a good quality bonding primer to ensure good adhesion.
You laid it on too thick, because nooks are tricky to paint for several reasons.
This was greatly exacerbated by not using primer.
Whenever the paint industry claims something, they mean it in a certain context. For instance I see a lot of brushes and rollers "for all paints". Yeah, they melt and come to pieces when I roll a marine LPU, because what ...
Might be caused by the second layer shrinking beneath the third layer because it hadn't fully dried.
In high humidity conditions, I generally increase the recommended drying time between recoats by 25%, just to be safe.
Alternatively, if the backside of the door has been stripped and hasn't been resealed, the door itself may be expanding slightly due to the ...
As far as UV resistance, you're in luck. Multiple coatings stack, so the silver coating you'll be overtopping will still be 100% effective on whatever UV (if any) gets through your next layers.
As far as reflective insulation, you have one choice: White with a 90%+ albedo. If your hope is to both have the roof reflect solar heat and also present multi-...
I use a shellac based primer for things such as this. It has better hiding ability then just paint or regular primer.
Give it two or more coats and see if it hides the problem and then you can apply the final paint.
If you still see a shadow after the shellac primer you could try a coat of bonding primer over the shellac primer.