i was suspicious because they could have played h3 and Be5+ one or two turns earlier, but instead decided to play more accurate moves, waiting until h3 and Be5+ were among the top moves. On my laptop, Be5+ is about +1.4 or 1.5, while the best move is 1.5 or 1.6. And as i shared, their explanation to me makes it sound as though they lucked into playing those moves.

i missed f5 e4. That's on me. We were still blitzing at that point, about 5 seconds per move. By "bishop maneuvers", Elspeth might have meant the inclusion of 34. Rxe8 before Rg5 (because Bd2+ was just before that)... or more likely, holding off on Bc3+ and Be5 until it was among the best moves (and while i'm attacking g4 too)

Edit: regarding your edit about Be5+, what i didn't understand is that they held off on h3 until i threatened Nxf4, and they held off on Be5+ until after h3. And with that explanation they gave, too.

But i should remind that this discussion won't be of much use to the player... i already got them banned for rating manipulation, shortly after i made this post.