Back when I was flush-trimming the arm and seat rail components, I avoided routing the straight edge on each where they would eventually be joined.   I could get a much flatter/straighter result if I trimmed those edges later on the table saw.    With a jig, of course.

I used a scrap of plywood with parallel long edges to make a custom sled for cutting the joint edges of both parts (one at a time, though).   I positioned the MDF templates so that the joint edge of each was flush with the edge of the sled.   To avoid any issue with the blade not being perfectly perpendicular to the table, I oriented the templates so that one had its right side facing up, the other had its left side facing up.  Any error in blade tilt would cancel out when the pieces were joined.  (I had installed the knock-down Domino hardware in the templates earlier so I could handle the two mated parts as a unit.)

I used some veneered plywood scraps from an earlier project for blocking, scribed and sanded to fit around the template.  This justifies my hoarding of scraps. 😁  Once fitted, I drilled pilot holes through the sled base, countersunk the holes underneath, and screwed the blocking in place. 

(Had I thought more about how much of the sled would be in contact with the fence prior to the saw cutting the work, I would have flipped the template right to left.   This would have resulted in more contact with the fence prior to the cut.  It probably wouldn't matter on a full-sized table saw, but I was using a small benchtop table saw.  Fortunately, it didn't turn out to be huge issue.   I just needed to be more diligent with fence contact early in the cut.)

Checking the fit with the actual arm piece.

Repeat for the seat rail on the opposite side.

Cutting an arm piece.

I had some minor saw marks on the first two cuts (the arms), but then some heavy marks on the first seat rail I cut.   Only then did I realize they were due to the cutoff sliver falling down into the saw, being caught by the blade, which made it deflect a little.  On the final seat rail, I pre-trimmed the edge on the bandsaw, leaving 1/16" or so (no sliver at all during the table saw cut).  The sled cut for that one was perfect.   I nudged the fence about 1/32" towards the blade and re-cut both seat rails.  This removed the blade marks on the one and ensured both rails were identical.

After the clean-up cuts, the joints were nice and tight.

8mm Dominos were very close to 1/3 of the thickness.

Dry fit, for now.

Getting closer.

At this point, I need to pause until I finalize how and when I'll attach the back assembly to the arm/seat assembly.   I would really like to weave first, then assemble everything.   This would simplify the weaving process.   However, it makes fastening the two main assemblies together more challenging because the weaving will be in the way.   If I fasten everything together first, assembly is easier, but I make weaving more difficult.   The decision also dictates the length of the back stretchers (assembly after weaving will require shorter stretchers for some wiggle room).  I've been pondering different ideas for this since the beginning of the project, and I need to make a decision shortly.   I have some hidden fasteners on order that might be what I need to be able to weave first, then assemble.  They should arrive next week sometime.