The half-elixirs naturally accumulate over time if you have the schedule to allow for using as much natural regen as possible, thus allowing as many events as possible to add to your supply. So fundamentally, it's the trade-off of my real life time for this supply ever since launch.

I want to say that I had about 300 something HE's a year ago, so I think that I've gained 1400+ since then. That would line up with events becoming more generous with the loot as well as the anniversary update to the gem gacha.
Regarding gemcha, I typically pull 50-60 times each raid, union, and off day. I don't pull during advents. The reason being that I pull using the gems from the guerilla quests, as I'm normally available for the evening period (I'm in GMT -5). So I set aside 100 AP to do 4 expert runs, then use either 2 or 3 half-elixirs for another 4 or 6 runs, depending on how many I pulled earlier that day and how I'm doing time-wise. Usually it's 2 HEs for 8 runs that day. Over the long term, I see gain in my HE supply. But since my gemcha pulling is relatively quite reserved, my weapon grids are actually underdeveloped for someone playing as long as I have.