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I'm editing a mesh with a Mirror modifier on the X axis. I want to apply To Sphere (Alt-Shift-S) to points that lie on the mirror boundary. I expect the whole shape (the part I'm editing and the mirrored part) to end up more spherical.

Here's a picture. In the foreground is the result you get if you apply it to half of the sphere. You can see that the boundary points turned into a circle but actually pinched in a bit. In the background, I just applied the mirror modifier and then used To Sphere.

Is there some way to get the more sphere-like result without applying the mirror first? (Keeping in mind the actual mesh is much more complicated: I'm not trying to just make a sphere-ized cube).

comparing To Sphere with/without mirror modifier applied.

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Put the 3D cursor at the center of your object and select 3D Cursor in the Transform Pivot Point panel:

enter image description here

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