If you can get it sorted, at the bit with 3 turrets, find the 6 crates in the area and build a 1-2-3 step thing out of them up to one of the balconies (I can only get onto the small one, but have seen screenshots of others on the larger one so who knows) then place 2 turrets by the rails, grab...
It didn't take that long for me, just shot away the barriers and then the core itself and that was it. Wasn't sitting there for ages just blasting it.
Do you use the balls to kill the gunships or can you shoot it with super gravity gun? (Long shot but I can dream :P)
At the start of the game, when Barney takes you into that room and takes off his mask, look through the little window of the door before the one you go through and there's a suit recharger.