Thanks! Unfortunately, I didn't have the reconfigured aircraft on the LAX-AKL segment. However, I did get one of the former First Class seats on the old aircraft, which was still very good. Plus, I had Business Premier on my final segment, AKL-BNE. ^

IIRC, the document I got at SFO was still labelled "Boarding Pass" and was printed on standard United cardstock, but I was told by the counter agent that it was not a BP (which I had to pick up at the Air NZ counter at LAX). I only got one for the LAX-AKL segment though, and not the AKL-BNE segment. And oddly enough, at AKL, the gate agent had some trouble locating my record at first, so not sure if that was because I didn't get any document for AKL-BNE at SFO...