What I'd do is - feed the Garmin power supply cable under the tank plastics from under the seat to the clocks area, mount the exposed 12v pin things into the 350 bracket with the supplier tiny screw & fit to the Ram mount.
Wire up your din plug with about 300 / 400mm of 2 core cable & crimp the other ends on to the Garmin supplied cable about 180mm from the small black box / transformer & cable tie this box out of harms way under your seat. Plug in your 12v din plug & it should work.