This might seem obvious, but I have trouble imagining that a pro would
even think about cutting this branch off all at once...

I've done this myself by climbing out on the branch with a chainsaw
and cutting off a section at a time (not enough at once to risk
catapulting myself across the yard). Even though it wasn't that high,
I tied myself off to the branch...on the correct side of the cut.

This was a thick, healthy branch where I had no question about it
holding me. I still wouldn't exactly recommend this approach...