When you say you want to "establish two bins", - that's where you've thrown a monkey wrench into the gears of the machine.
What you want to do is a simple, multi-key sort - which computers have been doing since day 1 after they were sorting.
All your "Rube Goldberg" machinations, are just stopping/slowing your effort.
Try and strip the work down, into it's smallest necessary parts. It's all you need, and it's also all you should want.