We Have Trim!
Another handy tool was the Midwest Products Easy Cutter. I bought it last year to cut trim for my dollhouse, but it works well for this trim, too, since it's just thin lattice. No sawing required with these babies in hand. Though Darwin did look like he was about to bust a blood vessel in his forehead once when he was trying to cut a particularly hard piece of wood.
The trim looks just as wonderful as I envisioned it would. This is the culmination of all my daydreaming about the kitchen:
Of course, things didn't go perfectly. We ran out of trim after only seven doors, so we'll have to buy about 20 more lengths. The buying is easy ... it's priming and painting them I'm not looking forward to. Will the painting never END?
I think I've been underestimating the magnitude of this project. But having some of the trim up makes it feel so much closer to finished.