Nice find! A rough TAS of that saves about 100 frames.
It seems you have to wait for it to go down a certain way before making it disappear, otherwise it kills you for some reason.
I tried avoiding the elevator all together by going backwards and clipping up the wall after getting the diamond, but no luck so far.
Still testing key first routes, but still need a faster route back after getting the diamond.
EDIT: I finally managed to clip through the vulture caverns wall. Now it is possible to enter the vulture near the diamond and exit at the vulture near the balloon.
The clip itself takes about 3 seconds, and its a long climb up (around 9 seconds), but this opens the door to new routes. My first idea is key first, then diamond, enter diamond vulture and go from there. Whether or not this is faster is still to be determined.
Current route:
1. vulture to balloon after diamond: 42 seconds
2. balloon to vulture warp after key: 36 seconds
3. entrance to medicine: 18 seconds
Potential route:
1. fall to balloon from start: 14 seconds
2. balloon up to surface: 33 seconds
3. diamond vulture to medicine:
So if the second route adds up to less then 96 seconds, it will save time.
The first part is roughly 14 from where the paths diverge.
Going back up will take some work. But a rough TAS looks like it will take 33 seconds to get back to where the route rejoins the route to get the diamond.
So about 47 of our 96 seconds is used. Leaving 49 seconds to get from inside the vulture to the medicine. Playing through by hand from right after the clip, it looks like it is going to be very close.
Another route idea I had, that probably is actually faster, is to use the diamond vulture warp after diamond and then exit right away at the balloon vulture and go get the key from there. I will test this now, but I am optimistic for at least 5 seconds savings.