I never thought I'd be able to get the Large Zenith Wyvern Gems but I'm finding great success hunting Apex Seregios with randoms doing the 1001 Shards mission. Challenging but not so ridiculous like the Apex Jho or Rajang...forget it!
Apex zinogre is the easiest monster and thus fastest to get them. Master's Test probably have a good chance, if you can do it this quest usually gives 2-3 Zenith Wyvern Gem L's and if you don't get those, you get Zenith Wyvern Gems.
Also this is my new FC: 4613-9618-3420
I've entered almost everyone with Mii's name on the list