For the open trees like a Sycamore, I use my son's Vortex, which is a Nerf type of minature football with a winged stem. I'm accurate and good for about 40 feet. Thus far it seems to get unstuck OK. It wouldn't work for denser growth tress. It's less forgiving than a small throw-bag when stuck. It falls into the category of being quick and dirty and worth having in the climbing tool box. For an open limb from the ground, it's the right choice.
I haven't used it in a multi pitched climb. However, I can visualize a greater freedom of motion with a football throw than a throw-bag/ monkey fist which will need some type of rotation before release.
The football idea sounds interesting. We might even be able to use one to have climbers in different trees throwing to each other...
How do you attach the throwline to the football - just tie it around the fins?
Because this isn't a life line, I use a clove hitch as the attachment of the Vortex football to the throw-line. The attachment is to the stem where the fins are situated. I figured that it provides a remote chance of beneficially becoming undone.
It has potential of being used in applications like climber-to-climber or in a gaming situation.