Never seen the brown paper. We do it ourselves and use the white wax freezer paper. We never have deer meat in the freezer longer than a year so can't really help with the longevity of it but it works great up to a year anyway.
Maybe you could just keep it the way it is and then wrap it in the white paper, double wrap it to give ya peace of mind. Kinda sucks to pay someone then take the time to wrap it again. But the papers 5 bucks and the freezer tape it 2.50 at wally world.