Horizontal metal framing drilled into basement walls. WTF???
Horizontal studding can supposedly result in savings on wall board which is why you come across it from time to time. If you really can't remove it you need to work around it. The downside is that this makes placing a moisture barrier tricky, but if you don't need that in your construction you can get away with fitting your insulation bats between the studs with an air gap behind. You need a vapor barrier on the roomside of your construction to stop warm moist air condensing in the insulation.
Are the 2 x 4's vertical or horizontal? I'm assuming the basement is concrete or rock. There was a time when nothing, not insulation nor wood were suppose to actually touch those walls, so the things like what you describe were done instead, as a sort of work around, leaving an air gap and such. It really doesn't matter at this point, it is what it is. Anyway to get a sawzall blade in there to cut one screw/bolt at a time? Pain in the *** I know.
Leave the framing in place. Foam insulation can be used to fill the gaps with no more 'damage' than a hole into each gap that is fairly easy to repair. Update: Foam insulation IS its own vapor barrier.
you NEED a vapor barrier on the outside of the insulation or it'll end up waterlogged and useless. In a basement, kraft faced fiberglass [the usual stuff you buy at the home improvement store] probably will NOT work well because you a) can't overlap the kraft paper behind the framing and b) kraft faced is not designed to repel actual water -- only moisture in the air. Talk to your home improvement sales guys for an alternate vapor barrier solution. Don't be very surprised if they tell you this project isn't a very good idea -- or if you need to use an entirely different type of insulation.