I'm mounting a GPS antenna closer to the center line, using the existing gusset/doubler as the backing plate. (Mine is a Garmin antenna, not Dynon, but similar hole pattern by the looks of it, same idea.)
I didn't want to center the antenna right on the stringer because the big hole for the BNC would weaken it significantly, like Stephen said. So what I did was to offset the antenna to the left by half the mounting hole lateral spacing such that the two right-side mounting holes are centered on the stringer and roughly centered between existing rivet locations, and the two left-side mounting holes, as well as the big hole for the BNC, are well within the gusset/doubler but do not go through the stringer.
Note that in the photos below the 5 holes (4 mounting holes and the hole for the BNC) are still just pilot drilled, not enlarged to final size. But you can see their locations (they are the ones that are not dimpled):
Top view:
Bottom view:
