Welcome to the starting point of hell for legit gearing. Getting past the 5.8 - 6k - 6.2(the usual ones used for 25m raids,and sadly 10m too because of "fast" runs - it's mostly just ppl want to be carried through 10m) barriers can be quite tough. Most guilds that actually do 12/12 require high gear as well,so that's not the easiest solution either(but still the best solution). My suggestion is getting your main set pieces via eof/voa,gathering gold for some boes/crafted gear pieces THAT FIT YOUR SPEC,and toying with gs for inspection(aka switch out proper gear to higher gs gear,pugs usually won't notice that your gs set doesn't have hit/expertise caps etc,just make sure you switch back for bosses). I'm going to tell you the truth,no achievments will get you past some of these barriers either,because achievments are meaningless thanks to the character trade.
Looks like you've never been to those raids. They're anything but fast paced and when(not if,bc of the player mentality on the servers) replacements are needed,they'll take anything between 30 mins to hours. All in all,the 29 emblems(at best) gained through those runs usually aren't worth the time investment for such overgeared folks,hence why you see them needing a lot of time just to get the raid full. I can make that 5-600 gold faster and easier than putting myself through all that with the gear they ask for,and i'm not the only geared player with that mindset.