Really interesting project there Warren.If my understanding of the way in which the tension is applied to the Skin is correct, then the loads applied to the Rings if they were replicated in Carbon would be Static Compression Loads. Its the bolts that are under tension. If this is the case then a composite structure(if designed correctly) should have no issues with those loads.
The form of the current Rings already creates a very "stiff" structure with the use of right angle returns etc very similar to a "box" or "channel section.
As you mentioned I would say the biggest issue would be creating a suitable thread in the composite ring to take the tension bolts. I have successfully used threaded inserts" Rivnuts" in Composites. These have the advantage that they can be applied to the part afterwards making the lay up much simpler.
Someone may be along soon with a far better answer but I think its worth a go.
Good luck and let us know how you get on.