Yesterday, in a comment, Debbie asked if I was going to strip the paint in the closet, and I have to admit I was tempted, but ultimately I decided I would rather apply my efforts to more visible areas.
Instead, I'm cheating and painting the woodwork with stain-colored paint. I put on one coat this evening and I'll apply another coat tomorrow. Then I'll probably shellac over the paint so it has the same sheen as the wood in the rest of the room.
There was one area on the inside of the door casing where Jeff had removed most of the paint, so I sanded and shellacked that area first before applying paint just in case I change my mind someday and need to strip the woodwork. =)
I did strip and stain the shelf board. I'll shellac that tomorrow along with the closet.