There's really no other way than to start shooting at them. Preferably from a distance and with a minigun or a rocket launcher which can blow up the Barrack OL's and Patriots quickly. All of the ones you do not blow up will start chasing you. Just make sure you keep calm. Their driving sucks so you can quite easily find a good spot to hide and then take out a few soldiers at a time.
Just wait for them to stop for donuts. You can blow up any cars in your way just by running over them, and you're less than a block away from your safehouse.
The easiest way to pass this mission without losing any health or armor and WITHOUT getting into a shoot out is to just follow the military until they stop at the Donut Hole in Little Havana and say the line of "go get some donuts soldier...sir yes sir...." then jump out of your car and hop in the tank and speed off to the lock up-simple and easy...I have pretty much never lost any health(still had 150/150 before and after) doing it this way. HTH
All I ever did was run right up to the convoy, shoot the turret guy in the head, then jack the tank, you might have to beat the door off with a melee weapon first though, it's been years I mean years since I played VC.
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