Your point that unitary evolution implies entanglement is certainly correct, however, when you say 'when you assemble an interaction, which tells you which spin particle has, you will have one OR the other value', this isn't possible unitarily. In as much as your postulate 3 leads to the outcome of any interaction being a single, definite state rather than a superposition, it explicitly breaks unitarity. And even so, since a definite state in one basis is generally superposed in another, you are not out of hot water here; if you invoke postulate 3 to force the state of two electrons after interaction to be |00> or |11> rather than the superposition of both, then in the {|>,|->}-basis these will be superpositions of all basis vectors in general.
And I must admit that I find your notation in equations (5) and (6) to be rather confusing. I guess you mean to say that in equation (6) the additional system does not 'know' about the state of the original system, while in equation (5), it does; however, such knowledge only occurs through interaction, and thus, without having interacted with the original system, the outside system does not 'know' anything about it in both cases (as is shown by the fact that it does not change its state).
How would you, in your formalism, model an actual experiment? On the traditional view, you have some measurement apparatus that interacts with the system in such a way as to reflect the system's state in its own state after the interaction. So for instance, a {|0>,|1>}-detector is defined by the equations
[math]|r\rangle|0\rangle\to|"0"\rangle|0\rangle[/math]
[math]|r\rangle|1\rangle\to|"1"\rangle|1\rangle[/math]
where |r> is some ready state of the apparatus, and |"0"> resp. |"1"> is the state in which it indicates the measurement result 0 or 1 respectively.
Now, using such a measurement device, I can retell the story I told in my previous post, where each of Alice and Bob have both a {|0>,|1>} and a {|>,|->} measuring device (the latter of course working analogously to the above).
Now the measurement device, if I understand correctly, is your external system |Y>. What difference does it now make whether it works according to equation (5) or (6)? In both cases, it does not seem to change state---thus, it measures nothing, and knows nothing about the system. So, how would a measurement apparatus that changes its state according to the above definition interact in your picture? How would it, in particular, yield the observed perfect correlation across both bases? Certainly, if your framework is adequate, there should be a way to mathematically derive these correlations, just as I have done above for standard quantum mechanics; I'd be very grateful if you could show it to me.