Clay,
I spent about 20 minutes at Ace looking thru the specialty hardware boxes. I found shaft collars with a 3/8 I.D and a 1/4x20 set screw. Since set screw thread is common, I'm thinking a simple thumb screw with 1/4x20 threads would work. I looked at plastic knobs with a threaded shaft, but they didn't have any small enough that would look right. That will allow adjustment once slipped onto shaft. Thats the easy part.
It gets a big trickier from here but still doable. Drill an 1/8" hole on the flat edge opposite the set screw. That should be fairly easy as long as the ID and OD of the collar are more than 1/8". Now the fun(hard) part. Drill a hole on the round edge perpendicular to bisect the first drilled hole. Tap the second hole for another thumb screw.
Insert the rod holding the profile plate in the 1/8" drilled hole and secure with thumb screw. This of course all depends on the size and hardness of the shaft collar. If you get one designed for a drill bit stop. It should not be too hard to drill and tap. This is just first round design phase, so feel free to run with it and modify as needed.
Next idea is to start from scratch with aluminum bar stock. It should
actually be easier to machine.