Aw, that sucks. I know I'm a hoot in a car chase and gun battle.
Surrounded by cops, and I'm a block away; do I whip out a sniper rifle? No. Do I try to snipe with a pistol? No. Do I clear them out by ramming into them with a heavy vehicle like a semi-truck or hummer? No. Do I take their car while they're distracted in battle by casually walking behind them; and then clear the area with their own cars, and run away off the nearby (rather high) overpass, and somehow get a couple of them to follow me like lemmings (car chase, of course)? Yes.
Personally, when it comes to GTA games, I prefer the most over-the-top method to getting rid of my problems over anything else.
For example, GTA:SA. Evade the cops by going cross country with a ***** rating with a BMX, and timing your run correctly enough to use the train pipelines as an escape while an oncoming train is charging your way. End it by making it to the peak of the mountain in the rural zone, and short-stopping the bike as SWAT and FBI cars fly off the mountain, and you casually bounce off the jagged edges and find a nice highway to turn into a high impact pile-up area (min. 25 car pile-up) to form a makeshift barracade, and KO some of them. Head back into Los Santos, and head to a building that allows base jumping, and go building hopping, and find a new bike to evade with. Lather, rinse, and repeat.
I think my best ***** run had to have lasted about 35 minutes like that. But with a motorized bike instead. Similar story.
My more awesome runs tend to use a fire truck as a primary means of plowing through barricades.