I had near perfect execution using this strategy and it ended up taking 1:27 between hitting the marker near the bridge, all the way up to when the mission passes. I had it recorded, but the video somehow became corrupted. I then timed a variation of the strategy we've been using and it took 1:30 between the same two points. For reference, in your video you hit the marker at 0:33 and mission passed occurred at 2:02, so 1:29.

I used the Taxi (Merit) with this new strat: Top speed: 267 km/h Acc: 10.7 seconds RWD

The Police Patrol: Top speed: 268 km/h Acc: 6.8 seconds 4WD

My opinion, it's not worth it to go for this strategy. Sure, it's likely you can get a taxi (merit) sometime before this mission and hang on to it from mission to mission, but I've still had it fail to go up the stairs even when I seemingly did exactly what I did other times when I made it up. It's also not the easiest thing in the world to hit all three guys in the train before you reach the point on the tracks where you're too low to hit everyone. I failed about 6 times before the first time getting it and even then I felt like I got lucky. You're definitely not in any better of a position to find a cab after completing this mission using this strat. A great cab spawn will still leave you waiting at the next mission marker (in my video, I didn't block the call so it took longer to come in) for a little bit for Call and Collect's text.

Here's the video of the 1:30 from marker to mission pass: