Backdrop Blitz: Maxwell Roth
A blitz assassination of Maxwell Roth in 0.6 seconds.
The key observation is that Jacob remains in the same position before and after the pre-assassination cutscene ("Burn, burn, burn!"). Ordinarily this position is wherever he kills the last of the four decoys. However, if the waitress poisons the fourth decoy then it allows Jacob to take an advantageous position.
This had the makings of a superfast blitz: Just stand onstage right behind where Roth spawns and mash 
, right? Well, Ubisoft must have been watching The Hidden Blade. They're on to our ways. If you stand anywhere onstage then the game teleports you, stage left.
I found another good position on top of the rear backdrop. From here you can do a double air assassination, shoot your pistol, throw knives or voltaic bombs. As a bonus, Jacob appears in the cutscene. Immediately after the cutscene the game resets your viewing angle to level. It takes nearly 3 seconds for Roth to spawn. I used this time to adjust my view downward and aim at his spawn location. His two bodyguards spawn first and are a little bit closer to the backdrop. It's easy for them to draw your aim away from the target.
It takes 2 pistol shots, 3 throwing knives, 2 voltaic bombs, or 1 air assassination to finish off Roth. I chose the pistol because it doesn't take any time to reach him. It took 0.6 seconds from the time Roth finished spawning until the second muzzle flare, after which he can be seen falling to the ground. I'm sure this can be improved upon. A head shot may kill him instantly.
Another advantage of the backdrop position is it affords an easy escape. Jacob is already facing the front door and can rope dart directly to the second floor balcony.
Instead of firing the gun, could you have jumped/dropped onto the stage for a superfast stealth assassination, or is there not enough time?
The best way to do what you're talking about is to start in the same position shown in this video and Free-Run Down (
+ 
+ 
) after the cutscene. There is time to reach the location just as they're spawning. My problem was usually getting a double assassination because the two goons spawn first. The double assassination animation takes time and doesn't look as awesome as a direct hit on the target. I did manage to get a solo stealth assassination once and even that animation took a long time. The bodyguards had enough time to enter Open Conflict and attack Jacob before the memory corridor.
I tried many of the same things you would have, Aurel. Besides the backdrop, I also had the Machinist lower the catwalk so I could perch/hang from it. My hope was that I could drop just before or during the cutscene like you used to do in Brotherhood. Hanging from the backdrop keeps you in the cutscene but the drop button doesn't work. Hanging from the catwalk or dropping (from either platform) just before the cutscene results in being teleported stage left. If you drop after the cutscene then you're facing the wrong direction. That's why I prefer perching and Free-Run Down.
You can blitz the Unique Kill from the catwalk, of course. I didn't find that very interesting.
This is definitely the fastest way to kill him and escape that I've seen, from the cutscene.
Is the time lost to poisoning worth trying something like this in a speed run? I would guess that it would be faster to run around and kill them all yourself than to sit and wait.
“Force has no place where there is need of skill." Herodotus
Thanks for reminding me. I forgot to mention that when it says "Watch waitress poison Roth's gang." it's more than just a suggestion. She will poison the gang on one side and then return to the bar where she will wait until you return to the rear half of the theater. This triggers her to continue poisoning the other side. I'm not sure if you actually have to look in her direction but that's what I do to know when she is deployed and I can make my way to the stage. If you want to play it safe you can kill the decoy backstage, return to the rear of the theater to trigger the waitress, and then climb the backdrop. That way if you get into a prolonged battle backstage you won't run out of time to get into position.
As far as a speedrun, I'd guess that you would avoid poisoning altogether (as well as the other two "assistance opportunities": usher and machinist). If you did use the waitress it would only be for one side while you kill the other three decoys yourself. Still, it takes so long for the poison to run its course. See DAZ's video, for example. He killed all 4 decoys with throwing knives in about 1:22 and ended up on top of a different backdrop. That's a more promising start to a speedrun than mine: http://www.thehiddenblade.com/ac-syndicate-final-act-non-lethaltargets-only