http://skyrim.nexusmods.com/mods/26355: A mod for wearing a user-defined number of rings.

DEPENDENCY:
This mod needs SKSE version 1.6.3 or later! In earlier versions the command RemoveSlotFromMask is broken and you'll not be able to wear more than one ring! Any SKSE version supporting Skyrim 1.8 will be fine.

RingLimiter allows you to have more than one ring equipped simultanously, what's the difference to other Unlimited Rings mods out there?

• While the basic mechanism that allows you to wear more than one ring is the same one (namely: remove the ring-slot dependence of the item), this mod adjusts rings on the fly instead of altering them in the CK. Thus rings from mods are covered, automatically, provided they have the 'ClothingRing'-keyword set and you and I don't have to worry about keeping the mod up-to-date.
  
• The mod keeps track of the number of rings you have equipped and will make sure you don't wear more than the number you've defined.

Important note: drop and pickup all of the rings in your inventory or you'll not be able to wear more than one of them!

This is a beta version, meaning I'll need feedback from you to make sure there is no ill behaviour I didn't foresee.
My concerns are mostly with potential incompatibilities to other mods that require a certain setting of the ring slot to work properly. Please read the corresponding notes in the ReadMe and notify me of any oddities you come upon.

Note on amulets:
At the moment I'm wary of expanding the mod to amulets. One reason is that the need is not that obvious, you having 10 fingers (at most) but only one neck. The more important is that, sadly, there is no safe way to identify them: most of the "items you hang around your neck" present in vanilla are 'necklaces' and carry the 'ClothingNecklace'-keyword. However there are some things called amulets (especially the religious ones) that don't have suitable keywords. I could handle the vanilla ones explicitely but this approach wouldn't cover modded amulets.

Miscellaneous:

• This mod only supplies the game mechanics. I've made no effort (no will I to display the equipped rings on your character's fingers.
  
• As stated in the ReadMe, when you try to equip a ring on the inventory screen but fail because you're already wearing your defined maximum, the 'equipped' symbol beside the ring entry will be shown regardless. The display will be correct the next time the inventory is opened.

Nice. Are you planning on incorporating amulets into this?

Not right now.
I'd like to be sure the ring part of the mod works as intended and for this I'd like to wait for some feedback results.

After that I still have the reservations stated in the OP, but I think, I could fabricate a Lore friendly explanation for going the easy way:

• Handle all items with keyword ClothingNecklace (like rings carry ClothingRing).
  
• This means: do not handle amulets. For the religious ones this would be ok because gods are jealous, 'thou shalt not wear an amulet besides mine'
  
• This also means: no handling of any other things worn in the neck slot but not labelled ClothingNecklace. I don't think many items will be affected but if they are we'd have to live with this.

Hrm, yes. Awkward.