An update:

I tried the PSM (Plexiglass Sheet Mount). I cut out a piece of Lexan, from Home Depot, that exactly matched the size of the cubby-hole. I then put 6 little plastic feet on the bottom of the sheet, and used the suction cup to mount the Garmin.

The suction cup adheres well to the Lexan. Reception however is nil in the cubby-hole, so I just grab the sheet and pull it forward until just short of the shift knob. This improves the reception, but I only get about half signal strength (because there is still a good chunk of car above it), and the updates to the GPS's position are somewhat infrequent. The convenience is great...since I can just push it back in when I park, and close the lid on the cubby-hole.

But, in the interest of science, I have just moved on to the PBJM (Peanut Butter Jar Mount). By foraging through the pantry, I have discovered that an 18oz Peter Pan (crunchy, of course) plastic jar fits the TCH cup holder nicely, the lid is very smooth for the suction cup, and the lid is exactly the right size for the Garmin suction cup.

I have just "installed" the PBJM, so will report back after some use. If it gets too wobbly, I will fill with some ballast, such as sand.

If my tight-wad solutions don't work, I will consider breaking down and spending 30-something bucks for a boring mount that actually works.