Do you not partially inflate the tube prior to tucking the tire bead under the rim? This prevents the pinch in the first place. Source: learned this handy trick

Do you not partially inflate the tube prior to tucking the tire bead under the rim? This prevents the pinch in the first place. Source: learned this handy trick in the middle of the northern Nevada desert, ~50 miles from anywhere during a cross country ride, from a perfectly-timed stranger riding the other way.