Lets all relax..
The mission was made easier in one of the updates - so I suggest that the OP makes sure that the game is currently updated [if you always have your console connected to the internet, it should be fully updated - if you never have, please connect it and the game will prompt if there is an update]
Even though many never had an issue with the chase before the patch, some did, which is why we had that update..
Best advice has already been posted - best to think ahead and try and cut the distance down.
"This land can offer something else than pain. You will give people hope. You will give people faith. They will fight and they will fall. But in time, they will rise for their freedom." - Achilles Davenport
"I realize now that it will take time. That the road is long and shrouded in darkness. It is a road that will not always take me where I wish to go. But I will travel down it, nonetheless." - Ratonhnhaké:ton
I wouldn't say notorious button. High profile yes. sprint button etc..
Edit: OP i don't think anyone commended you on your genius pun in "Lee way", truly you are a comedic god amongst men.
mah GTA online crew yo rsg.ms/1bNZIED