In a similar vein to this chain mail answer, but independently developped, I present:
Chain
Yes, the most overpowered piece of jewelry you could conceivably wear would be a chain, where each link of the chain has its own enchantment. Links are tiny rings. You could wear it around your neck, but that may not satisfy the "physical contact with the body" requirement. So instead, you wrap it around a limb, like a forearm or leg. Tightly enough that it doesn't move, but not so tightly that it cuts off blood circulation.
The main selling point here is you can have an arbitrarily long chain, carrying an arbitrary amount of enchantment. Links could be designed to be removeable in the field, and by in the field I mean at camp, using tools. You can break down a chain into multiple chains. You can include non-magical links for style or function. You can even go more two-dimensional and fashion your chain into chain mail. A chain mail sock or sleeve would already be more rings than you could possibly wear on your fingers, and possibly more magic than you can actually use.
It's very modular is where I'm getting at.
Of course, if you have an attunment mechanic then you don't have to fiddle with the links, you just pick which enchantments to activate, typically after a good rest/meditation.
Low inconvenience to the wearer while worn
You can wrap a chain around a limb which shouldn't restrict your movements. Depending on the material and how much chain you have, weight may or may not become noticeable. How comfortable it is will likely vary on the metal used and how you wear it. Obviously you'll have a problem if you start covering yourself head to toe in chain.
Low risk of falling off in intense situations
If you wrap it well enough, it won't fall off. You can also wrap a bit of cloth over it, or just wear sleeves or pants, so that it will definitely stay in place.
Ease of switching out for other enchanted items as the situation might demand
It's a chain. Replacing a link in a chain is doable, but it's certainly something that demands a bit of foreplanning. In a typical RPG, that would be done during a rest. You can split the chain into smaller chains that carry groups of enchantments that you commonly use together. You can then swap a bit of chain for another easily.
However if you have an attunement mechanic, where the wearer decides to activate an enchantment or not, you don't even need to bother with that.
Pros:
Modularity. Which means:
- Can be arbitrarily long, thus have an arbitrary number of enchantment.
- Links can have arbitrary size, limited only by the skill of the jeweler (for how small they can be) and carrying capacity (for how big and how many you can have).
- Can be split or combined at will.
- Can be made to fit pretty much any body part.
Won't hinder movement with the right configuration.
Easy to conceil, unless you infiltrate a hammam, sauna, swimming pool, or other similar venue.
Can be removed whole easily.
Is bound to look pretty sick when wrapped around your forearm or biceps.
Can be worn under pretty much any sort of cloth or armour.
Cons:
- Might require a minute or two to equip, so swapping chain in combat is going to be difficult.
- Requires some preparation to swap the links, so definitely not possible in combat.
- Is probably going to be more expensive than rings.