I just got curious about the effect of non-inertial motion (aka falling into a black hole) on entangled particles. I found this http://prl.aps.org/pdf/PRL/v95/i12/e120404
(Alice Falls into a Black Hole: Entanglement in Noninertial Frames
, Fuentes-Schuller and Mann, PRL 95, 2004) - it turns out that entanglement is observer dependent, and the accleration degrades the entanglement seen by one observer falling into the black hole, and the other just escaping.
So, there's that.
But yes, hardly the most important problem in the OP's "experiment".