Currently there is a bug i noticed with troll archaeology which will help leveling archaeology quickly. As we all know recently they buffed archaeology which gives 3 times (15 points) the level up on rares. So far troll only has 1 rare which is the epic weapon Zin'rokh, Destroyer of Worlds. Anyways back to the bug. I've noticed that when you get to Zandalari Voodoo Doll which is a common item it also gives you 15 points and only cost you 27 fragments. Just stay on Eastern Kingdoms and you will level archaeology quick.
edit: Adding the list for troll archaeology. The one that is underlined is the one that also gives you 15 points instead of only the Zin'rokh and how many fragments are needed for each item to give you an idea on how fast troll takes to solve.
Common tier Troll items: 14 common items
Zandalari Voodoo Doll - 27 fragments
Fetish of Hir'eek - 30 fragments
Eerie Hakkari Idol - 35 fragments
Lizard Foot Charm - 32 fragments
Jade Asp with Ruby Eyes - 35 fragments
Feathered Gold Earring - 34 fragments
Cinnabar Bijou - 35 fragments
Atal'ai Scepter - 35 fragments
Gahz'rilla Figurine - 35 fragments
Skull-Shaped Planter - 35 fragments
Bracelet of Jade and Coins - 35 fragments
Drakkari Sacrificial Knife - 35 fragments
Tooth with Gold Filling - 35 fragments
Fine Bloodscalp Dinnerware - 32 fragments
Rare tier Troll items: 1 rare
Zin'rokh, Destroyer of Worlds - 150 fragments