Checking my Understanding of Bell's Theorem re:Free Will

I just wanted to check my understanding of Bell's theorem as it pertains to the assumption of free will. I'm familiar, from other discussions, that there has been subsequent work which effectively demonstrates that free will is a necessary consequence (or a necessary part) of Quantum Theory - the set of results/theorems referred to as Kolmogorov embedding*.

*I say that as though I am very familiar with Kolmogorov embedding :P


I just want to check if my understanding, to date, of Bell's theorem re: free will is accurate. I will set out my understanding in a set of ordered statements in the hope that it will make it easier to identify any inaccuracies.

(Btw, is there a way to write special characters like lambda EDIT: other than copying and pasting?)

1. The preparation of the particles is a function of λ.
2. λ itself is a function of everything in its past light cone.
3. Therefore, the preparation of the particles are a function of everything in their own past light cone (including the past light cone of λ).
4. The measurement settings are not a function of λ.
5. The measurement settings are a function of everything in their past light cone.
6. If we go far enough back into the past, the light cones of the measurement settings and the preparation process (including λ) intersect with a common cause.
7. This common cause would explain the observed correlations.
8. Therefore, either the measurement settings or the preparation process needs to be screened off from this common cause i.e. the chain of causality needs to be interrupted somehow.
9. Usually, this is simply assumed i.e. it is an assumption so pervasive that it is difficult to see how we could engage in experimental science without it. [Quantum Nonlocality and Reality: 50 Years of Bell's Theorem [edited] by Mary Bell & Shan Gao (p.242/243)]
10. Isolating the mechanism for choosing the measurement settings from the preparation process doesn't screen either off from the common cause in their past light cone - it means, perhaps, that the common cause event is located further in the past light cones.
11. Without some kind of "circuit breaker" event, to interrupt the chain of causality, the assumption of statistical independence appears to be unjustified.
12. The free will of the experimenters is invoked to justify the assumption, because "free will" is the only conceptual idea we have that necessitates non-correlation with events in the past light cone.