You are right, it is very tricky! For example, if one follows Penrose and considers the proper time difference along the same worldline due to different entangled states curving the spacetime slightly differently being a cause of decoherence and therefore collapse of the wave function. The wiki writeup is at  https://en.wikipedia.org/wiki/Objective-collapse_theory. My personal guess is that if the Anton Zeilinger-type experiments are scaled up to the Planck masses (~10 microgram), we will either hit the decoherence limit or can be quite sure that objective collapse is not a thing.