16/20 Is where I felt like I started to hit a wall in terms of frequently getting a pristine though I suppose it is all chance. After reading forums I feel very fortunate to have had some 20 achievements left when I got the title because I keep reading these posts about people that are 20+ in each and still missing 2 - 4 pristines. After I got my title I went back and finished a few 20s though it might be equally annoying because when I was down to just need to collect 20 of the pandaren type and I had to keep skipping Mogu digs, or do them just to create a new dig and hope it was Pandaren.
Tips
* Any challenge mode you've beaten in Gold rewards you a teleport path to its location you can use to move around the map quicker, this is a shared 8hr cooldown between all dungeon locations, but still useful for 1 quick easy teleport.
*Use your hearthstone! Personally I set mine to Shrine of Seven Stars for convenience because this seems to be the most centralized location relative to archaelogy digsites.
*Stock up on those lodestones that teleport you to a random digsite. You can purchase them for 1 crated artifact at the turn-in location, you can only carry 20 maximum but they are nice to have for a quicker grind.
* Also buy a few maps that randomize digsites. These also cost 1 crated artifact. I can't recommend these as much because they remove 1 digsite as well and sometimes the new dig site is in a crappy spot. But if you have Dungeon Challenge Teleport/Lodestone/Hearthstone all on cooldown and all your digsites are far away this is when I would use it.
*As with any grind, find some good music/podcasts/videos, something to keep you occupied as this is a fairly lengthy grind.