After forming a daisy chain in a line, treat it as *new line* and form a second daisy chain with it. This makes the overall daisy-chained line shorter but fatter.

Also, over 45 years ago while taking junior life saving, we were taught to make a ball of line that fed from the inside of the ball. I believe one could hold onto the free end and heave the ball to a person in need. However, to rewrap/recoil the ball would be more tedious than stacking the line back in Tom''s stuff sack.