Problem: You are lowering your partner with a broken leg down 300 feet with 2 150 feet ropes tied together and you get the knot and the partner can't take the weight off
Possible Solution: Tie a Prusik knot in front the the belay device and attach that to your harness. Cut the rope behind the Prusik knot, now you can free the belay device. Untie the cut rope and the full 150 foot rope and tie a bite in the end of the 150 foot rope and attach it to the Prusik loop. Set-up the belay device just after the bite and detach the Pruisk loop from your harness. Contuine lowering. Myabe use 2 Prusiks if you have them