I've followed this thread with a lot of interest. My basic problem is that the rope supplied on my HH is 1600 lb test polyester, very stiff, and not suitable for attaching to the rings.
I have some BPL AirCore Pro URSA, rated at 1400 lbs, very lightweight and flexible, and experimented with that. I cut some cords, put bowlines at both ends, and attached the rings by a larkshead, and around the hammock body just behind the Hennessy wrap knot. I found that a Prusik knot does a much better job of holding the rings together than the Larkshead. But the way I attached to the hammock is a hack, and I'm unclear what impact that has on the structural ridgeline. Furthermore quite a few posts on this thread suggest that unbalanced pull by one end of the cord on the rings may contribute to ring separation.
So I cracked the cover on the Hennessy wrap to see what we've got.
Here's what mine looked like
The main line goes through the top hole (can't see this in the photos, the entry point is at the back), is wrapped three times downwards, run through a second hole (same orientiation as the first; the pictures show the exit point of the lower hole quite clearly)
brought back up being tucked under the first wrap and passed through the
(black) loop that anchors the structural ridgeline (this is seen clearly in the second photo). Then a bowline is tied around the line at the entry point (most easily seen in the first photo).
My AirCore is a lot thinner, but I can solve two problems at the same time if I double it up---put even pressure on both cords forming the Prusik knot, and integrate the ring assembly into the HH layout. So I cut 4 ft of cord, put a Prusik knot around the rings at the center, then used the two ends in the same way as the fat line in the HH cord. Here's a picture of the rings, and the cord after being wrapped, but before the bowline tie-off.
I then tied off the end cords with a bowline. Had to slip some cord around to get the knot close to the hammock and without long tails. The AirCore is very smooth, and that part is easy. The nearly finished product looks like
All that's left is to cover the with caseing and secure that.
I've quite enjoyed the various tips and experiences offered on the hammock forums. Thanks all.