That's the thing about Tenex, You don't have to think much about it.
Friction hitches are loaded way differently than bridges. The concentration of force on a bridge ring is very high, it's half your body weight focused on a few square millimeters. I use two rings, it helps some but doesn't actually change the bend radius, just separates the bend into two components.
My opinion is, use whatever you want for the material, but don't cover it. Technora won't fail catastrophically under body loads without showing a lot of wear so, as long as you watch it and replace it when starts to fray, no problem. I'm liking Polyester and webbing at this point. I don't know why my BFII bridge wore out so fast but it sounds like most don't. I would have never tried making one otherwise.