The problem with my handwave is that the very first instance of the NCC-71807 is from before Data reports that the downloading of the Yamato
logs "should be in our computer by rendezvous". Does that mean the downloading is incomplete (meaning no problem) or that it has not yet commenced (meaning the data aboard the E-D should not be corrupt yet)?
But Picard does appear to be viewing a report of the malfunctions currently plaguing the sister ship, thus he has received at least some data from that ship, thus the corruption probably has already taken place. Yet the other problem relating to this first scene is that it's done with an immobile, backlit Okudagram in a shot where the camera moves; even if there is to be a rewriting of all the 71807s (save for the frankly invisible one on the saucer) into 1305-Es, will the blu-ray people be bothered to alter this graphic? The rest of the problematic logs are pasted on Picard's desktop monitor in postproduction and will need some extra work in any case, and odds are that the registry in the Observation Lounge will be cropped off the picture due to the different format...