The factory recommends installing the transponder antenna on the bottom of the boot cowl near the transition from the boot cowl to the fuselage fabric. It appears that on the 2007 S7S model they have modified the boot cowl, adding a foam/composite core to the bottom to improve strength/rigidity. This had the side-affect of making the bottom of the boot cowl too thick for the standard stub antenna mount, or for any other transponder antenna mount that I can find.
The "fix" for this is to recess the stub antenna in the bottom of the boot cowl, bringing the base of the antenna up to the ground-plane mounted on the inner surface of the boot cowl. I used a forstner bit to create a 3/4" hole through the composite material to the ground plane, then mounted the antenna directly to the ground plane material.
I also spent a half-hour or so doing general cleaning of the interior of the cockpit, removing metal shavings, composite shavings, dust and accululated debris.
