Well, after seeing
this and not seeing an improvement to that forthcoming...
Have a WIP (GG version).
GH1: 0:19.
GH2: 0:22.
But most importantly...
B1: 0:20! (matches TSC time)
Fun fact: I stumbled across the precise technique for achieving 0:20 completely by accident. I had a WIP with 0:21 and was going to show everyone, but discovered that the input for the run up to the fight in GH3 had disappeared(!?). I reran that segment and spliced it back together, then discovered it would desync just as I was making the critical jump in B1... so I began tweaking the input by hand and suddenly and quite accidentally triggered the result you see! (I'm afraid to mess with it more, lest it breaks again...)
EDIT:
Now to the end of Bridge 3. Have fun slogging through the auto-scroller.
EDIT2: mike89 noted (on IRC) that he thought it would be slightly faster in GH2 to slow down a bit going into the final ramp so as to catch less air time.
He was right, to the tune of 17 frames. Splicing the improvement into the run didn't quite work - in exactly the same fashion as before, and generated an even better result in B1 for a 15 frame improvement there! B2 is desyncing badly, so this movie only goes to the end of B1 (I'll post more WIPs later).
EDIT3: Silly me; I forgot to roll down the bridge at the end of B1 while working with the improved glitch. So,
I went back and fixed it to the tune of another 27 frames. So close to 0:19 :-/