Q: Late 2014 iMac with recurring Magic Mouse troubles

Magic Mouse seems to be fighting with Retina 5K iMac. Symptoms include:

• dramatically accelerated (or decelerated) motion
• occasionally loses, then immediately restores BT connectivity
• cursor stops tracking completely

Rebooting iMac seems to temporarily resolve. Power cycling the mouse seems to temporarily resolve. Replacing batteries (despite 80-100% battery life claims) temporarily resolves the issue (perhaps since it's a mouse power cycle). Genius Bar replaced the mouse - no change in symptoms. Apple Support suggests bringing the whole iMac into see the geniuses. Since that's kind of a heavyweight process (literally!), I thought I'd ask here to see if others have seen similar symptoms or might suggest a more convenient next step. Suggestions appreciated.

-D