I think this might be a little faster than the current strats, but I haven't timed it properly.

Getting the bike there is really easy, you drive along the wall and just jump off, no need to break.

ETA: For anyone who doesn't wanna watch this on a potato - https://dl.dropboxusercontent.com/u/60029413/gta-vc%202014-06-03%2023-17-19-362.avi

Now it's been pointed that this can only work if his starting position is far back, which doesn't happen often. However I found a way to consistently make him start far back.

Now do you notice how I walk really slowly into the cutscene and therefore am far away from him when it begins? I think that his starting position correlates with how close you are to him in this cutscene, which in turn depends on how you enter the cutscene. The testing I've done confirms this theory. This makes sense from a developer's POV - putting everyone on a level playing field

So if you sprint into the cutscene (no matter which elevator), Tommy gets right next to him and when the chase starts the guy is already a mile in front. If you walk normally he's a little bit further back but it's still hard to hit him in the corridor though I think it might be doable if you're skilled. If you do what I did (walk very slowly into the cutscene) then Tommy is really far away from him and it's pretty easy to hit him.

Obviously going up the elevator to the right is easier because you're closer to where you need to jump off.

And this also means that there's a bit more set up time, but I think overal it should be a bit faster than normal strats

I took the liberty to upload it to Youtube

or if you want to upload it to your youtube here are the encodes I made before uploading to YT (11MB files), you shouldn't try to upload lossless video files because it's slow and most of the times they doesn't work.

https://dl.dropboxusercontent.com/u/27816146/mamamia1001%27s%20Time%20saver%20for%20Mall%20Shootout%20%28letterbox%29.mp4 (4:3 aspect ratio)
https://dl.dropboxusercontent.com/u/27816146/mamamia1001%27s%20Time%20saver%20for%20Mall%20Shootout%20%28widescreen%29.mp4 (5:3 original aspect ratio)