After drilling the doublers to the fuselage (not sure why I didn't get a picture of that), I tested the fit of the antenna. This one had some silicone sealant lumped under the sticker, so I peeled the sticker off and cleaned the base up with a razor blade. It rests much better on the bottom skin.
I left a message for Don at Delta Pop Aviation to ask if I needed to seal up the hole in the base. He confirmed I did.