I'm not 100% sure that I know what bulkhead is. But, I'm thinking that we may have something similar in one of our bedrooms. If I'm totally off on this, then sorry in advance :)

In my dd's room, which is downstairs, we have a piece of her ceiling that is lower than the rest. It's where the ducts and pipes, etc. run through. We couldn't decide how to paint it either.
We ended up painting the ceiling portion of it the ceiling color, and the drop portion of it the wall color. My reasoning was that all vertical walls should be the same color, and all horizontal walls should be the same color. I completely made up my reasoning though, so I don't know what the proper rule would be. I'm also thinking that if you have actual lights on the horizontal wall that it would be best to paint it your white color to make it appear brighter? Again, just guessing here :)
Here is a picture....it's kind of hard to distinguish, the wall color tends to reflect onto that ceiling portion in the photo.

Your reasoning makes total sense! I was leaning in that direction but needed some reasurance. Thanks for your input. I love your doors! Did you do the writing (Megan) freehand? It's beautiful! Love the chandelier, too!

I could tell better with a photo, but I think that I would paint the whole thing DB.