Alternatively to the +3 minus some stuff as an in-between thing, you could create a selection of +2 that have bonuses random things.Maybe something like+2 strength and bonus feat: called shot+2 dex and +2 hide, move silently, and tumble+2 con and +10 hp+2 int and a bonus level x spell slot+2 wis and +2 will saves+2 cha and x bonus to turn undead checks. These are not well thought out, just examples, and I'm sure it would take some work to make them balanced between each other. Alternatively, they could just give bonuses to a few skill checks of the relevant ability.
I would say Disarm for the STR ring, but it's even more useless than Mobility (for DEX).