Hi Akinbo; and thanks for the "naive" inputs, for I'm very much from the same school myself (as you've no doubt seen).
Thus: my use of the term "Lorentz invariance" simply echoes Bell's desire to Bell's supporters. My own terminology is "a fully relativistically covariant formulation" so I'd be pleased if you could expand on your alert. Especially if you thought that there were situations where my own term failed.
Now as to those socks. Can you access Bell's Bertlmann article and Bell's sock analogy therein? [Please let me know.] And can you be wary of that term "measurement"? For I'd like you to seriously analyse the sock case yourself; then get back to me.
HINT-1: Do not subjugate your naivety! Consider, for example your statement above: "... Alice measures her sock." Does Alice know that it's a clean and present sock before "measurement"? Or before the post-person shoves its parcel into the letterbox?
And what if the person who sent the sock to Alice had made it from the finest thread -- such that it's impossible to tell the inside of the sock from the outside? And what if -- in the post-person's haste to deliver, or in Alice's rough haste to unpack the parcel -- the sock was unwittingly turned inside out?
HINT-2: For, reversing the analogy: I trust you can see that the interaction between a spin-half particle and an SGD is far more disorienting and lasting to the particle than an accidental turning-inside-out is to a special sock.
Enjoy! And please stay in touch so that our shared naivety keeps flowing; Gordon