This really seems a bit too random. I got 6-7 Great Spiritvein Gems (2-3 drops, 2 carves, 2 rewards) at once against a Tempered Lunastra the first time (with Geology). I thought Lunastra might give more of them for some reason, slayed 2 more and tried breaking just parts and maybe I got 1-2. The first 4 Tempered Elders I also got only like 2 Great Spiritvein Gems in total.
Though I did get 3 from a captured Tempered Rajang and the occasional one from Tempered Savage Deviljho partbreaks.