Once you get to Algonquin (the central island), you can legitimately access helicopters - either by stealing them from the helicopter tours, or by having Brucie ask you if you want to go on a helicopter ride (if you have done all his missions, he should call you shortly after you went to Algonquin for the first time) - naturally, you can also phone him and select the heli ride yourself. Doing this during Brucie's activity has the added benefit of the wanted stars disappearing if you get back to his heli pad afterwards.
While you still can't get to the last island, you can get a six star wanted level just by hovering too close to the blocked island. But instead of hiding, going to a safe house, or flying around for six minutes, why not put that time into getting another trophy?
If you haven't started to work at the Under The Radar trophy yet, it should easily take you six minutes to fly under all the bridges. Just remember not to hoover too long in the same place, lest the choppers start firing away at you.
I actually got this achievement in the X360 version by accident while going for the Under The Radar achievement. Once I saw my wanted level rise to six, I figured 'why not?' and kept on going from bridge to bridge, occasionally dodging helicopter fire. I did this on Brucie's helicopter ride so without guns, shouldn't be too hard. Now I have the game on PS3 and I did it this way again on purpose, again with Brucie. I didn't even have to dodge helicopter fire this time around, they never got close to me.