I rerolled my hunter/druid/monk for soothsayer's epic, and the highest count I hit was roughly 16 before i got an epic proc. I did this a good amount of times hoping to double proc epics but lost interest. The same for a stint a i did going for crossbow of the hand, i never had a bad streak for an epic proc go past roughly 15~. Those are both green quest items, so the proc to epic isn't 1/250 or whatever. I truly feel every 20 you'll see an epic proc. I probably saw about half my attempts remain green, and around 25-30% of them went blue. More ancedotes, but I don't think quests follow the same rules is what i'm getting at. If anything, maybe there's a bad luck protection setup on the first epic proc, then chance to proc another epic drops past what it starts at when making a new character, which would better explain how much trouble you had with back to back procs. So say it's a sliding scale of 1-10% (this is just random numbers for ease), you start at 5% chance it'll go green to epic. After that, it slides back down to 1%, and after xyz quests, it slowly raises again until another epic rinse repeat.
Just an idea, they do have the bad luck protection in existence already, and we all know your first legendary was much faster to acquire during the first of legion, then the 2nd plummeted to barely anything until you did enough to get it back up. So the system does exist anyways, who knows if they used it.