I've slipped through so many barbed wire fences it's almost secod nature. Just push down the strand that's crotch high and swing a leg and torso through in one smooth motion. I sometimes snag, but it's just a slow-down, not a stopper. On the tighter fences, I'll sometimes take off my Tshirt so it won't snag, even so, most of my ugly work Tshirts have little holes on the back.

I guess you could always carry a narrow 3 or 4 foot roll of carpet. Throw it over the top and slide over the top like all the prison-break movies. It could double as your sleeping pad.