Thanks guys, I'll keep practising it like that. I tried again this morning and it was easier, and that last practice was "one of those" in other ways. I was tired, and fitting it in because my other half was watching some nonsense on TV, and I was also trying to ignore the fact that my fingernails were too long, but I was too lazy to stop and trim them!
I understand the argument that the 4 2 3 1 fingering fits the phrasing, although it is perfectly possible to play 3 1 3 1 with the very same phrasing, it's just a skill one would use in other circumstances anyway, but perhaps it is more natural.
I also have a slight reservation about the argument that one changes position three times while playing the four notes in each, which suggests the hand stays still each time then teleports to a new position instantly. In reality, the hand is moving up the keyboard to some extent through each "position", also turning, etc., to accommodate the motion. However, what I found after some 3 1 3 1 3 1 practise is that I more easily lost track of that upward motion and missed keys.