The helm Scold's Bridle is not on this list because (from what I can see) there is no way to use it while being able to cast skills (does not work with blood magic or 100% reduced mana cost). Because of conflicts with Soulthirst and/or flasks the following are excluded as well: Coralito's Signature, Gluttony, Doedre's Elixir, Lavianga's Spirit.
There's usually no point. If you can get enough reduced mana% so that your skill costs 8 mana you're already very close to 100% reduced mana cost and might as well get that without giving up your ring(s)/amulet. including an upcoming 3.0 expansion that will bring .
I think you're confused about how stacking things works when there's a limited amount. You pay more opportunity cost to get that than just one mod on a ring/amulet, as you're likely going to need to path somewhere else to get that last bit. I've tried several times to make builds with 100% reduced mana cost, and unless you've figured out a way to reliably use the 50% reduced ascendency, you're spending a ton to travel and pick up jewel slots.
While it's not guaranteed, increases your mana cost so much that you probably wouldn't terminate Soulthirst with your mana regen during flask. Also doesn't introduce the ramping problem you'd have with Indigon, though you'd probably have to invest in regen pretty heavily to not need Soul Taker.