Hello Doug. Welcome.
What fascinates me about the origami jib is its uncanny resemblance to the usual much more complicated-to-make 45 degree shelf jib, when inflated.
I'd like to try one on a dinghy. Paul admits to an unavoidable small wrinkle near the luff, but it probably doesn't matter, and I can't see it anyway, in the photos (JRA Mag #85) it looks pretty good.
Doug, for a full size sail it is said that its best if the orientation of the cloth is parallel to the leech of the sail, so if there is batten rise (which seems to be usual) it may not be quite so simple to make full-width-cloth panels as you describe - you'd need to check that with someone who knows more about sail-making, I am not sure. (I notice Paul's origami "hybrid" rig seems to have zero batten rise.)
Doug, also you may not be aware, but the SJR as designed by Slieve already eliminates all those hauling parrels you refer to. The sail design/top panel/yard attachment point are worked out so the sail drapes properly without them. (Well, almost). Instead, however, you still have to have two paired-spanned-parrel-downhauls (see Slieve's notes for explanation) which need to be attended to when reefing. I suspect a dinghy with an un-tapered tube mast would probably get away with very short standing batten parrels - but might still need downhauls, I haven't tried it yet.
I think the Origami rig can be further simplified. Does the D-former actually make any real improvement, in practice? I doubt it, and would far prefer to keep the plain full length battens as in the SJR (spit junk rig). KISS. A tiny little bit of asymmetry doesn't hurt, and I bet you couldn't tell the difference between port tack and stbd - I can't anyway. And although the D-former might eliminate the need for batten parrels, I suspect downhauls MIGHT still be needed - it would be great, for a dinghy at least, if downhauls too could be eliminated.
I see Paul's origami jibs, in a SJR arrangement (with full length battens and not the D former), with short standing batten parrels and PERHAPs just one spanned-pair downhaul (hopefully not even that) as a starting point for a hoped-for dinghy rig which could be quick and easy to make - and able to be assembled or dismantled in less than 2 minutes. So far its just a daydream - nothing actually tried yet.
By the way, I've never had a fan-up with my Amiina Mkll SJR - touch wood! I currently remain hopeful that the planform eliminates it - maybe I'd better not speak too soon! Jami? Edward? Dave D? James? Any fan-ups yet?