Have you been to the proving grounds yet to try a role you normally don't play? Trial Master Rotun seems awfully lonely in his little corner of the Temple of the White Tiger with everyone so busy collecting Timeless Coins or sieging Orgrimmar. What about flexible raiding? Have you tried taking the step up from raid finder?
Blizzard has sent a clear message with patch 5.4: they really want you to get out of your comfort zone.
Nobody is forcing you to, of course, but more tanks and healers is a great thing for the game, and they can be just as fun to play as DPS. The proving grounds may not turn you into a seasoned tank or healer, but at least you won't walk into raid finder for your first tanking or healing experience completely blind. The fear of being yelled at or blamed for a wipe is what keeps a lot of people away from the support roles. No one will be yelling at you in the proving grounds ... except for yourself, of course (damn you, endless mode).
Don't forget, in proving grounds your gear is all downscaled to ilevel 463, so you won't be at a disadvantage for trying a new role without shiny epics.
Remember back in Wrath when Icecrown Citadel pugs were commonplace? It was the only way to raid outside of a guild group, and ICC 10-man filled that niche very well. The combination of increased 10-man difficulty and punishing raid mechanics in Cataclysm and Mists was the death knell of raid pugging. Raid finder was never truly a replacement. It's a great system for those who don't like to commit to a schedule or just enjoy the convenience to see content, but it's just not the same as getting together with friends and struggling to down a boss.
If you focus solely on raid finder, I think you ought to follow Blizzard's urging and give flexible raiding a try. Worried about the commitment factor? If you can't show up it usually won't be a problem with the flexible size unless you're a tank (this is why we need more people to try proving grounds tanking). If you're running late, fear not, the rest of the group can still start without you. The best thing though? If it turns out you like the organized raiding experience, you will already be ready to jump into a normal mode raid team because all the mechanics are the same. If you're interested, you can start by watching your realm's trade chat or Timeless Isle general chat for a group. Failing that, you can check out WoW Insider's handy guide to using the oQueue addon for flexible raid groups, or visit openraid.us / openraid.eu.
You might be surprised at what you discover by stepping out of your comfort zone.