Hi, I have what is hopefully a very basic question. How do I move the points in the red center group so that they form a perfect circle, but shifting as little as possible from their original positions? The type of thing that would be done in Blender etc. with a spherize / circularize action. The points are already flattened in the y direction.

My vex isn't great yet. I did consider getting a normalized vector from the center for each point, which would be ok except the distribution wouldn't be even around the circle. I also considered using sin / cos to reconstruct the x / y positions for each point, but this would twist them away from their current locations, needing to be rotated back by an arbitrary (i.e. non-procedural) amount.

try using Circle from Edges maybe

@ryuku Exactly what I was looking for - thanks!!!

Though I've realised I've been really dumb, since I started with a sphere I should have just grouped the parts I wanted to scale to the oval shape! duh … but Circle from Edges is gonna be really useful to know about anyway.

don't blame yourself nice you came to it
just for collection maybe - there is smth else under RMB > Make Circle or Shift+C maybe at once will be handy too

Select the edge loop and use Edit SOP.
It works on points, edges and primitives.

Ok, reading your question again, I see what you want. Scale will get you what you need.