Because of the cargo bag mounted to my seat post, I couldn't use the Quarter Turn Seat Post mount to install the Varia Radar unit. Luckily, on the back of my rack frame, there's small, flat, vertical area that is ideal for the Varia to ride. Since none of the two mounts would affix to this flat, vertical area, I set about modifying the factory included Stem Quarter Turn Mount. I have a lathe so I chucked up the mount and parted off the rubber extensions. Then I faced the remaining surface flat and parallel with the other side. Using the two small Allen screw holes in the mount as a guide, I drilled holes through my rack flat area. I re-threaded the Stem mount screw holes to U.S. 4-40 and finally screwed the puck-shaped mount to the rack using medium strength Locktite. If anyone would like this done to their factory mount, I'd perform the mod for $5.00 and you pay round-trip shipping to CA.
I had a somewhat similar situation, except my mounting location would only accept vertical holes, which means that the Varia would be 90 degrees off if I did it like you did.
To remedy this, I removed the Allen screws from the quarter turn-mount, thereby getting to the base underneath. I drilled two holes in the base (so now the base has four --two original Garmin and two 90 degrees that I made. Re-attached the quarter mount to the base and voila!
I don't have a lathe, so I used a Dremel to cut off the part of the original mount that was not needed.
