Stiv said you can actually make the final jump without ground pounding with his strat, so that's likely fastest.
This video http://youtu.be/Ef0mHJrr_ig?t=10m19s is likely is fastest method to get the jiggy on top of mumbo's mountain without talon trot. If it's possible to get it in talon trot it MAY be a bit faster though.
As for beak bombing with the snow, there might be a use for it other than what was used in the current TAS, but I'm not sure where
If we suddenly start considering this run an improvement, then I have a question: what exactly prevented doing so in the initial submission? If nothing, then there's no point in "obsoleting" it. Otherwise I can make 100 submissions of a single game with slightly edited endings, each of which would be "more entertaining". And I'm not even mentioning what Masterjun can do to abuse such an approach.
Drifiting and all that should influence the RNG because it'll pull a different amount of numbers for graphical effects.
Based on that (granted, it's a single sample) the item seed seemed to depend somewhat on jumping. Not sure what to make of that.
We've already arranged to be able to lose arbitrary items (other than bulky equipment like armour) on the way up through the dungeon, so it's quite easy to get rid of conflict after the Quest without losing time. However, Astral's proving more of a problem.