I think I see the solution:
1. Remove the 4 bolts holding down the rail (tagged as Item 3 below). Odd headstyle - Guess I'll need to buy a new socket to match.
2. Remove the entire rail assy
3. Insert the clip/bracket into the front-end of the trim piece in advance. There is a locking tab on the clip to be aligned with a slot on the trim piece. Ensure proper orientation/alignment of the slot, like the top photo above.
4. Set the rail/fitting assy onto the roof, over the mounting studs, just to the rear of the front stud.
5. Slide the rail/fitting assy forward along the roof to engage the mounting studs, front and back. The rail assy will only slide as far forward as the rear-trim piece slot will permit (see bottom photo above).
6. Confirm a secure fit, then insert and tighten the 4 bolts.
Hopefully: No adhesives are involved.