This has not been intensively tested (lack resources) so everything I say may not work universally.
So, after literally 4+ years of never posting, I find something I can share:
REQUIREMENTS:
At least two characters at either level 70 or level 80 (different accounts required).
HOW THIS WORKS:
Arena teams can only be created at level 70, 80, and 85 (seems like atleast, not intensively tested)
Arenas can be played in the brackets of 70-79, 80-84, and 85 (not tested below 80)
WHAT YOU NEED TO DO:
1) With characters at a previous level cap of 70 or 80, create the arena team you want to gain rating on.
2) Level the characters (you could do this with only one character theoretically because of the level difference) to the top of the arena bracket level cap (79 for a 70 team, 84 for an 80 team).
3) Que for arena and dominate the usually only lvl 70s or 80s who are queing usually just to see what the arena is like.
4) Repeat step 3 until desired rating
5) Level to 85
NOTES:
You will not be gaining conquest points at non-85 arena brackets.
You will not be gaining personal exp.
You will not be gaining honor.
You CAN gain gexp and grep.
This ISN'T something that will happen overnight. More than likely this will have to be assisted by wintrading if you want a 2.2k+ rating. I haven't gone through all the steps myself (lack enough accounts) but queing against other players will not be quick. There just aren't enough people queing at higher ratings.
You will be better off if you wait until you can win your matches at high ratios (90%+) and in winning streaks. If you que below arena bracket cap, you will probably meet higher levels and get owned.