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Keep the rope bag, tie a 'slip hitch' where the rope exits the bag and clip a biner onto 1 of the webbing handles after clipping into the slip hitch. This will eliminate the rope falling out.(It happens to most of us using rope bags) Keep the biner clipped onto the webbing strap while doing the entire removal. Then all you have to do is unclip the slip hitch.
I start with a Husky 346XP 18" (narrow kerf chain) and depending on what I need next, mostly the Husky 372XP 24"(semi-skip chain), or Dolmer 7900 32" (full skip chain). Using a climbing saw is a big waste of time, IMO. How many cuts are 14" or less?
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Are you sure that's such a good idea?
Your climbing rope is supposed to be your escape route in case the sh*t hits the fan and you need to relocate yourself in a hurry. Having a tied-off slipknot directly below your friction hitch kinda locks you vertically into the position where you are making the cut.
I always make sure that I can quickly pay out slack if something goes wrong - In crane work, there's plenty of potential for crushing injuries if you're hanging out near the cut, you definately need to be able to move downwards quickly, using only on hand.
Think ahead!