Seems like there is some work in progress that will improve the features available for configuring gestures on mice from within BetterTouchTool as well!
Yes, I'm currently working on a big upgrade to mouse support, hopefully being able to completely replace e.g. the Logitech software. Limiting to a specific mouse will be part of that.
However it's part of a massive feature as I'm porting libratbag/libratbag: A DBus daemon to configure input devices, mainly high-end and gaming mice (github.com) (a comprehensive Linux mouse driver library) to BTT. So it will still take a bit. The next alpha version will already be able to do something like this, but it will be a bit complicated to use.
