Enjoy the thrill of the chase, don't just end it ASAP! If you just follow the target in any GTA4 chase mission, you will get a longer and more enjoyable mission. (Except where you get a bonus or time penalty, for completing the mission in a certain time frame like in TBoGT).
Why not do a test run before you do your final save to move your game-missions on. Play through the same mission a few times (and perhaps even record a video of it, in case something unusual or funny happens).