Ok, here are the stats I collected when doing blacksmoke mountain runs. I think I've done enough to comment on what the trend looks like.

The baseline drop rate of ichor for the quest seems to be about 50%. Although I had good and bad streaks along the way, I ended up with 13 drops in 28 runs initially. It seemed to hover around this ratio, so I feel pretty good it's about 50/50.

I also tried a bunch of runs with a shamrock elixir. In that case, I got 15 drops in 21 runs, a significant improvement to about 70%. I haven't done enough runs to be sure of the boost, but it sure seems like running elixir boosts the drop rate. There was at least one other player I ran into who had a similarly high ratio with elixir on. I'd love to hear if others have seen this too.

I also noticed that there was not a single pink drop in all of these 49 runs. That's not impossible to believe of course, but that's a total of 245 rolls of the dice without a pink, not even counting the rerolls from luck elixirs (I got one reroll every time of course). And at least some portion of these runs (maybe 1/4) happened during the first few hours the map was out, which has traditionally been the highest drop rate times for new content. I wonder if the drop rate is somehow broken or accidentally (intentionally?) set extremely low. I ask because nearly every expansion has some kind of drop rate tweaking done to it to make it "right", so I'm suspicious that this place will be no exception.