Regarding a cross pole between the tops of the trekking poles at the transverse peak line, Version 1 shown in the yellow string prototype photos in the OP was inspired by the Black Diamond Distance Tent, which has a rigid “bridge” aluminum tube that inserts into their dedicated trekking pole grips or can be used with adapters for other brands. I had designed a CF tube bridge with adapter for that version before ultimately deciding on different designs that don’t require the extra weight (and pack space) of a bridge.
One of my basic design ideas is analogous to merging two single-pole shelters side by side. With a single pole shelter the single pole is tied out in all directions 360*. By having two poles tied out in all directions 360* its basically twice as strong but without doubling the loads. So rather than a weighty and clumsy bridge, for a small fraction of the weight you end up with a much stronger structure.
I’ll definitely be testing the Dyneema cord to DCF bond, in various configurations. I also have a few ideas about how to tension the cord and the DCF during fabrication, and we’ll see how those work out. I don’t want the cords to move at all relative to the DCF because I think that will cause abrasion and slicing issues.
For bonding mesh to DCF see cubenmaker.com’s experience.
All my tent/tarp designs use the trekking poles in the upright position with handle up and tip down (no dirt or water on the grips, no chance of tip poking through material, downward tips dig in a bit like stakes) so there will be a means of fixing them in place at the proper locations in the peak.
I definitely plan to make catenary cuts, although with my current cutting pattern that requires only three separate pieces of DCF the only location for such cuts (aside from the bottom edge all the way around) are the two long seams that run the length of the tent along the longitudinal ridge lines:

“Another way you could accomplish something similar would be to layer 1/2″ wide (or so) strips of DCF along the lines you wanted the dyneema cord”
That sounds like what I was trying to show in my sketch above for bonding cord to Dyneema “At Panel Corners” unless I’m misunderstanding your description.