I used a 1/8" radius round-over bit in a palm router to ease the edges of the weaving slots.   Nesting the rails together provided a stable platform for the router for the two inner rails.

The backrest was nearly ready for glue-up.  The joints were tight enough that they didn't require a lot of clamping force, and Bandy clamps worked fine holding the stiles in place when they had square edges.   I wasn't sure if they would be as effective once the stiles received the edge bevel, so I tested with a beveled scrap first.  The clamps still worked just fine.

Before I cut the bevels on the stiles, I dry assembled the two backrests and marked the direction of the bevel on each stile end.  Without this, it would be easy to cut the bevel the wrong way.  (The dominos are not exactly centered, so there is a definite front and back side to the stiles.)

With all the bevels cut at the table saw, I re-assembled one of the backrests and wrapped some Danish cord around a section of both stiles near a rail.   This allowed me to check for fit between the arms.  I figured that I would need 1/8" clearance on both sides (1/4" total) to account for mounting hardware.   With the wrapped cord pressed against one arm, there was a gap of about 1/8" between the cord and arm on the other side, which meant I need another 1/8" of clearance.   Back at the tablesaw I re-cut all the bevels, removing 1/16" material from each stile, and glued-up both of the backrest frames.

The mounting hardware bought from Amazon are cabinet pivot hinges.  This may not be my final solution, but they allowed me to keep moving forward.   Because the mounting holes will ultimately be covered by the Danish cord, I wasn't concerned that I might have extra holes in the stiles if I switch hardware later.

I started by bending the hinges to match the bevel angle.

The hinge plate will eventually be mounted over top of the cord after the weaving is complete.

With the hinge placed at the midpoint of the stile, and a loop of Danish cord as a spacer, I could mark the location for the screw holes.  I transferred the marks the opposite stile, drilled pilot holes, and attached one of the hinges.

On the arms, I drilled a 1/4" hole for the hinge pin.  I did not use the bushing included with the hinge because it had an diameter that didn't match any of my drill bits, and I didn't want to have it too loose or too tight at this stage.  Since I may be changing hardware before all is done, I figured it was best to drill the smallest diameter necessary for a test fit.

I used a couple of tape-covered washers to center the backrest and keep the hinge plates from scraping the arms.
The pin from the mounted hinge slides into one side, and the loose hinge pin into the opposite side and then it's screwed to the stile.

With the pivot sorted, it was time to do the final shaping of the frames.  Rasp, scraper, and sandpaper.  My old familiar friends.

Progress so far.

I'm now at the point where I need to finish all the sanding before the final glue-up.