I think 170' has good advice here, & mathematical formulae to back it up! I don't do production long-lining, so when I get asked to perform I'm usually a little out of practice. Providing I don't need the length for obstacle clearance, I use our shortest line (50ft) when placing objects down when there is no-one on the ground to assist as I find it easier for me to control, & 120 ft when there is some-one on the ground to asssist as it makes it easier for them to control. I haven't done many tower constructions, but acknowledging up front that the riggers will need to control the load in all directions except vertical & planning for that might help?
P.S. - By the way "beater", apt name. I'll bet it came naturally to you.