Looks great Shawn! Good technique as well.
I’d do it almost the same, but with only one mesh..
Make a loop cut on the ‘cylinder’ and slide it into place. P > Separate by Selection. Take that new piece in Edit Mode and delete one vertex (where overlapping should occur). Convert the Mesh to a Curve and extrude the overlapping end:

Then you can model the band straight (as one piece and a bit better than I did here):

and add a Curve Modifier:
