For enchanted jewelry:

Ring of sleep, on use operates like a sleeping bag with a limited number of charges before disappearing.

Ring of unnoting, on use turns a stack of notes into actual items, with a limited number of items converted from notes before disappearing.

The running from combat just seemed like an interesting idea, slower fatigue rate is the simpler option.

Ring of unnoting could be used to bring a stack of food in notes and unnote them as you quest or PK, or unnote ores to superheat if youre mining, for example.

For team skills:

Level 80 Smithing, crafting, fletching and cooking could give a small percent chance of duplicate items like extra bars or bows.

Level 80 agility could give a slower fatigue rate, or a chance to run from combat in the 2nd round.

Level 80 theiving could give more gp or items per npc theft, or a chance to have a player killed drop 1 more unprotected item on death.

Level 80 firemaking could give a chance to make a fire without consuming a log.

Edit:

Alternate smithing, crafting, herblaw or fletching team skill bonus at 80 could be building an item with a % chance of not using all materials. LIke fletching a mage log might not use up the log, or smithing might use 1 fewer coal for a bar, or 4 bars for a plate.

Smithing could be a good idea maybe a percentage chance to get extra bar when smithing whatever you're smithing?
Cooking could be the same like cook an extra shark or swordy by percent of skill over 80..
Fletching is a tough one.. Maybe extra arrows created? or percentage chance to not use feathers, tips, or shafts.
I like the idea of lower fatigue for agility. it needs some point to the 80.. I really don't think there is 1 right now.
I like your idea for thieving.. maybe make that +1 item only in team deathmatch versions of pvp.
Firemaking is cool as well. Hopefully we bring in ability to burn higher level logs and that plays a part in firemaking.. Making a fire yet keeping your magic logs for a second fire.

The note ring has potential, but make them rare and a limited # if uses. like 50.. or 100.. So they have a use, market value, and are a commodity.
Sleeping bag ring could be useful to skillers. that dont want to carry that extra inv slot for sleeping bag. as above.. make it like 5-10 uses, rare drops, etc.. Could eb good for the economy..

I +1 these ideas with tweaks and edit's for more team skills. Economy boost as well when teams want higher stats sometimes they pay higher prices for a skill. Maybe even make some kind of team skills challenge between 2 teams instead of just pking.. Kinda like they had the team wars in rs2.. just a rs1 version would be pretty sick..