Well that was weird - I was struggling to get a crank puller into that quad chainring. It kept cross threadding and not sitting right. I tried cleaning the crank threads, grease, oil, and it wouldn't go right. So after a while I tried another identical crank puller and it went straight in.
Both crank pullers have perfectly OK threads, the ones in the crank are a bit munched with age, but it just worked on the second, and not the first.