Thank you for the image, ahanford.
The change of the points will lead to a change in the shape.
There is no native function nor a tool that would do that.
What you can do is to run the
Main Menu> Mesh> Move> Iron (I would suggest using 50% and 180ยบ)
many times over the selection, until it comes close. The shape will flatten.
Alternative:
You could select the edges, use the
Main Menu> Mesh> Conversion> Edge To Spline
Set the spline to To something round that is close to your shape’s profile, e.g., B-Spline.
Then place this into MoSpline as Object> Mode> Spline and set the MoSpline> Spline> Generation Mode to Even and the Count to the point count you need.
Now you can use the Snap options [3d/vertex] and place them precisely.
There are certainly other ways, but I find them to be more an effort than the one described above.
Perhaps someone has a modeling plug-in for that, but I haven’t tried (e.g.: HB_EvenDistribution or HB_Relax, @ Hello Luxx), nor being aware of it.
All the best