True. I implicitly assumed free localized electrons with similar momenta when I made my statement (something I shouldn't have done).
Keep in mind though, that from a QM point of view, even unlocalized electrons are considered identical until a measurement is made, at which time they are placed into a position and/or momentum eigenstate (one of an infinite possible allowed number when in free space) - this imparted quantum "number" then gives a unique identity to the particle. You are right in this - free particles do not have discrete position/momenta spectra.
On these threads it's common to find the belief that random processes have no cause, or that random is a cause.
QM (Bell's inequality, etc.) only shows that random processes have no localized, physically measurable cause. It says nothing about globally hidden variables. (Then again, this starts getting us into the realm of the metaphysical and unmeasurable.)
All processes are random. With such phenomenon as EPR, all such system states began in causal contact. The spacelike "comm" between the 2 particles is simply due to phase shifts in an existing field. No energy exchange is necessary, because that was done when the field was established. The field and it's properties are the cause. I see local as defined by the boundary of the system, in these cases of spacelike separation of bound particles. That's, because the state isn't a function of distance, only E.