Is Cmd-Opt-arrow supposed to move off-curve handles symmetrically about a smooth on-curve point?
I’m finding if I Cmd-Opt-arrow one such handle it moves by itself, but if I do the handle on the other side, both will move in or out together.
Either this is a bug or I’m misunderstanding/misusing the modifier keys.
You mean, Ctrl-Opt-arrows.
Seems to be new, I didn’t know it myself. 
Anyway, here’s how to reproduce:
Start a new glyphs file and go into editing a glyph.
Draw an ellipse with the Primitives tool, switch to Select tool, and click off shape to deselect.
If you Ctrl-Opt-Arrow or Ctrl-Opt-drag the handles that come before each node (e.g. the right one on the top node), the handle on the other side moves symmetrically. If you Ctrl-Opt-Arrow or Ctrl-Opt-drag the handle after the node (e.g. at the top, the one on the left), it moves independently.
this is actually really nice. a bit weird that it only works on one side though.
whe i followed your workflow, eliason, I moved the top right off curve anchor as you sad. all same to me. but them, when I moved the top left off curve anchor (from the same anchor), i could move the whole anchor-to-anchor-stick through the top anchor as one thing. this could also be very usefull, but I could not redo it afterwards.