App or Script to Move a Window Between Desktops With Only a Keyboard Shortcut?
Thanks to Lauri Ranta finding some further related questions that I didn't, I came across SizeUp, which does what I'm looking for (and several other window management tasks). I was hoping to find a more lightweight solution (I already have one window manager running full time in the background), but this will do for now. It's also unclear how well it works in Mountain Lion. I've only tested under 10.7 so far, but I saw some reports that it had issues in 10.8, but nothing definitive.

If anyone comes up with a different/more lightweight (i.e. an app that just does this, or a script), I'll mark that as the accepted answer, but for the moment it's SizeUp.