There are two ways for you to interface with the JC trainers in HH/Thrallmar:
1. Talk to them and say you wish to train.
2. Talk to them as a vendor and browse their goods.
I believe both will only sell (as vendors) gem recipes for green gems, unless there is a limited recipe I've missed.
As the trainers, you should be about to train on heavy fel iron rings etc. They have recipes available up to 330-335 (can't recall which.)
To get my druid to 335 I did it by cutting green quality gems and selling them for 5-6g or mailing to friends. I didn't write it down but I think gem cutting went green for me at aroun 335 and gray at 350.
You can also obtain recipes through reputation. I believe HH has some for friendly/revered/exalted. I think there is one for revered at Cenarion Exp, and multiple ones with the scyers. I'm still 65 so I haven't looked into consortium rep ones yet but I think most of theirs are meta cuts, which you can do at 360-65.
To get from 350-365 sucks... I had to buy several blue gem recipes and offer free cuts for skillups. On my server even rare cuts (+8 agi etc) will only sell 40g, the raw stones sell for more. So I have only cut enough for skill ups.
I hope you are a miner. I am a miner plus I have a 65 miner hunter alt. I constantly smash Adamantite for gems and last night I got (from one 20 ore stack) 3 living rubies, 1 dawnstone, 5 green gems, and dust.
Sorry for the ramble but I hoped this helped. Save ALL of your adamantite dust because you need a lot of mercurial adamantite to get from 365 to 375... when even blue gems go green (yet to get a skillup since it went green.) Now I make the minimalistic mat based jewelery and have advanced to 370 mainly with some nighteyes and a lot of eternium and mercurial adamantite.