You guys absolutely nailed it. Took all the gaffers tape off the handlebars and cleaned the area with brake cleaner. Cut about a 12" length of innertube and split it so it was flat. Wrapped it nice and tight around the handlebar on each side for the 2 clamps and held it tight with a small strip of gaff tape. Installed and took it on a 25 mile test ride today...solid! Didn't move one bit with a Garmin and phone attached.
Thanks so much!