In reply to Twiggy Diablo:
Quick and dirty (read tedious and inconvenient), take it off and dangle it from harness.
Or depending on your ropes, consider using one rope as a haul line if not already in any protection.
Or take it off at the constriction, fix it to some pro and let a second send it up on one of their ropes.
Ideally you would want to see the constriction coming and haul both the leader and seconds pack after leading the pitch. If it gets snagged, second retrieves it on the way.