Well - time for an update on the strengths and weaknesses of this mod after a full season of use.
It worked out mostly the way I wanted it to, but there were two main problems.
Problem #1 was that the adhesive holding the velcro to the awning eventually failed.
Problem #2 was that it was trapping water. The sunbrella wrapped entirely around the rolled-up awning, and any water that made it into the rolled up awning stayed there.
I corrected both problems this week. I got some double-sided 3M outdoor mounting tape to stick to the awning. I spoke to the people at the company and they assured me it would work. I also cut the awning cover shorter so that it does not go all the way under the rolled-up awning. That way water will not get trapped.
-Speak