thats mostly what ive been doing, on SotA im usually in tank or on turret so i contribute as much as anybody else, and on Eye of the Storm im capping :D
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Dont the tanks/turrets scale with gear? Especially the demos are super easy to kill if a no GS person is in/on them.
To answer, start with the ICC repfarm to get your ring, farm fos/pos/hor nm, then heroic, get the trinket from toc 5 man, do WG quests and do the BG itself as much as possible to get the WG trinket (if you can get into a group to voa). Then do heroic rdf if you have a healing or tank offspec using the same gear you have on to farm the mainset. Do 10 arena losses every week (you can try to win but it will take way longer) just to get some AP, then start farming BGs to get relentless or wrathfull offpieces.
Farm either 10k gold or whatever battered hilt goes for nowadays or try to get into pugs or buy the furios weapon with vote points.
The, either consider donating for a weapon, play to 1800+, get into pugs. Same with trinkets, although its worth mentioning that being a non human is a giant advantage over being a human gearing wise, at some points honour is worthless for gearing but nonhumans can buy a bis piece for it, humans have to do pve or donate.