Thanks to all who advised. Long-term, I think that adding a KlickFix or equivalent mounting system to the bag is what I'll do. Looks like costing about 50 bucks.
For now, I decided to see if I could mount it to the rack and seatpost. Using the two fixed parts of the camera bag's 3-piece shoulder strap and two nnylon MTB toe straps, I did this:
It fits tight, doesn't wiggle or sway, and looks great on the bike. Only downside is that the very stiff leather lid is right up under the saddle, so it doesn't open all the way. If that turns out to be really irritating, I'll try to solve it, but for now, I'm going to ride it like this. (And clean up the leather a bit.)
Thanks again for all the help,
--Shannon