Handing in
Silithid Carapace Fragments is no longer possible as of Cataclysm. Supplementing trash farming with Fragments picked up from the AH would have made things slightly easier though.
Instead, post-Cataclysm, assuming you are getting boosted and can take any piece of gear you desire, the fastest way to reach Exalted would be to save your insignias until you reach Neutral, and:
1.) Stock up on extra quest items required for your armor pieces - those quests provide 500 base rep each.
2.)
Armaments and
Regalias are another source of rep, each hand-in providing 500 base rep each. Each hand-in requires either an armament or a regalia and 3x
Elementium Ingot, but they are usually found dirt cheap on the AH these days.
3.) Once Neutral, don't forget to go talk to Anachronos in the Caverns of Time for a ring of your choice. Both the initial quest and the following upgrade quests provide reputation.
4.) Cross your fingers that
Artifacts drop. Those are worth 1k base reputation each, but are somewhat rare to find off trash.
5.) Handing in the
head of the last boss in AQ10 is worth a one-time 500 base reputation, while the bosses there provide a miniscule amount of Brood rep too on death. I'm talking 50'ish reputation per kill, so I wouldn't bother unless you just need that last bit, but chances are you will more than cover it with AQ40.
I'm not sure when this was changed, but lately I've noticed that bosses throughout the dungeon provide 500 base rep each on death, PLUS the insigina. It used to be only C'thun who would provide reputation on kill - and 2.5k if memory serves me - but not drop an insignia in turn.
In just 2 full clears, as Human with the Guild 10% rep boost, I've gone from 0/36k Hated, to 12.5/21k Revered on a new 60 twink project of mine.