Well I can think of several different ways of rigging the strapping on the tube frame, but most are sup-optimum in terms of strength. The strongest stitching method wouldn't work with a closed-loop seat frame, can't stitch the stuff on the frame. That grommeted system pictured above is a way to work around that constraint.
BUT, the strapping could be stitched off-frame IF the tube framing is designed in a manner that unbolts in halves, akin to a bolt-in segmented roll cage. IF the frame tubes could be unbolted removed, the sewn strapping could then be slipped on / woven in place. And the frames slipped and bolted back together and back into the overall seat structure. That would make the webbing portion much easier to accomplish.
And the bracketry / clamps that hold the tubing frames would have to be placed to not interfere with the strapping, match the spacing of the strapping.
PM me and we'll talk about the particulars. I'm running back and forth between Temecula and Lompoc, out of Santa Clarita, the rest of the year. Swinging by your place can be arranged on either end of the Temecula runs. Aint that far out of the way when I swing thru the Wrightwood area / 138/18. Or you can mail me a couple 4-5' long strips of that webbing to start experimenting with. I can bend up some EMT conduit as a mockup frame to work from.
in fact a seat panel hoop could be done in a big 'C', joint at the back bottom in a supporting clamp, and the strapping can be slid on and woven on thru that gap.