Tower of Despair is fast becoming my least favourite raid due to the number and specificity of the rings. The result is:
1) A high proportion of raid loot going to the vendor, either directly or "when I get the one I really want".
2) Players getting to 20 completions with nothing to show for it.
My suggestion is to stop treating the rings as raid loot and instead treat them as ingredients: Make them bound to account initially and bind to character after crafting. The 20th reward list could then be changed to be similar to Shroud: +2 and +3 tomes with a small chance at a +4.
This would make it easier to form groups (ala Shroud) and reduce the number of rings which go to waste because noone in the group is the right build for one that drops. I don't think this would make it too easy to acquire rings as more people in the group would be interested in each one that drops.
This suggestion is based purely on my own observations so I'm interested in any and all feedback!