So I'm willing to do it correctly, but I want to do it efficiently.
I'm also going to try this Minwax Antique Furniture Refinisher product to see what exactly I'm dealing with on the existing doors and trim.
I simply sanded half of the back of the test door this weekend to bare wood. Then 1/4 of it I hit with 220 sandpaper and the remaining 1/4 I didn't sand at all. I did a combination of regular stain, gel stain, and just poly on the door in various applications.
The best looking was the sand to bar wood and restain.
I'm going to give the other side a shot with the furniture refinisher and a Polyshades Natural Cherry finish. That may give me what I'm looking for.