Hi Peter,
Nice essay both stylistically and the topic although Bell's theorem type discussions can be a bit tricky.
First you seem to want to have some "classical" picture of spin. This swims against Pauli's dictum that to consider spin as "an essentially quantum mechanical property,... a classically non-describable two-valuedness". In fact Pauli may have oversold this point of view since in fact there is a way to view spin (to some extent) as an "orbital angular momentum. There is a great article by Hans Ohanian in the American Journal of Physics entitled "What Is Spin?" (Vol. 54, page 500 (1986)). What Ohanian shows is that if you look at the energy momentum tensor that results from the Dirac equation there is a rotating energy density of the Dirac field which gives one an angular momentum of hbar/2. One can run similar arguments (and Ohanian does) for Maxwell's equations and photons and in this case the rotating energy momentum density gives an angular momentum of hbar instead of hbar/2 -- different equation different magnitude for the internal field angular momentum, but the point Ohanian makes is that spin really is very similar to classical angular momentum. Thus trying to give a "classical" picture of spin works.
Next I like your "classical" example of the spin 1/2 property that you need a 720^o rotation to return to the original state. I hadn't seen this before. If you have access to Kerason Huang's book "Quarks, Leptons and Gauge Fields" he offers up another "classical" example of this. If you can find the book he gives pictures of this (which are much better) but I'll try to describe what he does -- take a rectangular piece of cardboard and use a marker to draw an arrow on it along the long axis of the rectangle. Next attach four strings to each corner of the rectangle and then tape/attached the other ends of the strings to some surface/table. Twist the rectangle around 720^o (so there are 2 twists in the strings). Then by passing the rectangle under/over/above the lower/upper strings you can undo the 2 twists! The last part of the description is bad which is why it is good to have Huang's book since he shows the step-by-step moves you need to make. However there are only a limited number of moves one can do so by playing around with it you can quickly figure out what moves are required to undo the 2 twists.
Finally you might find of interest the recent EPR=ER paper by Susskind and Maldacena (ER here means Einstein-Rosen bridge). "Cool horizons for entangled black holes", Juan Maldacena and Leonard Susskind e-Print: arXiv:1306.0533 [hep-th]. They are looking at the firewall puzzle and are proposing that there is some connection/entanglement between particles via an ER bridge connecting the two. This was sort of a "classical" entanglement flavor with classical in scare quotes since wormholes/ER bridges are not exactly classical.
Anyway nice contribution to this topic.
Best,
Doug