your going to want to use in a few spots, but ...
It should be possible to not have a heavy weapon for the PS3 version (PC360 there is a save editor / Coalesced editor to remove it). I haven't tried this but in theory it should work. First make sure you dont have any DLC that has a heavy weapon in it, that means no Cerberus network (arc projector), Terminus Pack (Blackstorm) because this adds it to your inventory. Now, on your new game don't pick up any heavy weapon or research any. This should work, give it a try