I did a little bit more research and got some part numbers for other strapless tankring bags that fit the RX3. I haven't purchased or tried these, but they're designed to fit the same 7-bolt bikes as the SW-Motech Type 115, so they ought to fit.
Both are less expensive than the SW-Motech bags and twist off to remove, unlike SW-Motech's cable release. Givi has a lot of bags to choose from. Cortech just has the one bag with an optional GPS add-on as far as I can tell.
Givi
Cortech