What I ended up with...
I went with the RAM ball mount and attached it at one of the fairing attachment points. It took a M5 x 50 bolt and a washer, and I put a #10 x 5/16" x 3/4" long spacer through the barrel of the mount to keep the bolt snug. I can see why RAM did not suggest this mount for the bike - there really are no handlebar bolts where it can be mounted.
I have to say the hardest part of this installation was running the wiring harness. Garmin complicates it by including separate microphone, headphone, and antenna connections in the harness, but the splitter is halfway down the harness, which is now somewhere between the side panel and the fuel tank. If you actually wanted to use them, I don't know where you would leave the ends to make them convenient. I just bundled them all up with tape and covered the ends.
Thanks to everyone for suggestions!