Indeed there are different sorts of entanglement and unfortunately now you really are on the edge of science so we are still trying to quantify it.
Probably most updated discussion on the web
=>
http://phys.org/news/2013-06-spooky-action-physicists-entanglement.htmlThe extension of understanding entanglement is how it was deduced that you could entangle two particles that never existed at the same time. Time-separated entanglement was predicted by even original early quantum theory it has taken significant advancement in QM however to finally be able to show it.
The simplest forms of entanglement work exactly how you describe but that is not the end of the story it is simply the easiest case or mode of entanglement. If you think about it you have an obvious problem your simple entanglement requires even particles because you are swapping spins so how would I entangle 3 particles they would have to ping pong or something like that
Hence we did an obvious test way back in 2008
=>
http://physicsworld.com/cws/article/news/2008/jun/05/multi-particle-entanglement-in-solid-is-a-first
An international team of physicists has entangled three diamond nuclei for the first time.
The fact you can entangle odd number of particles tells you something significant that entanglement is definitely not as simple as you have tried to make it.
You are open and smart enough to understand the science and experiments so turn your thoughts to Quantum Spin and what it is and I am sure this will all start to make more sense.
