Is there a way to rotate an edge loop but have it constrained like the edge slide function?  To explain what I mean you can see in picture 1.  I  have an edge loop selected.  In picture 2. I have rotated the edge loop 45 degrees which results in a squashing in the mesh.  Picture 3. shows the result that I am looking for.  The edge loop is scaled correctly on the X axis before the rotation so that there is no squashing after the rotation.  I can work it out mathematically to determine the edge loops scaling factor before rotation but I was hoping there was an easier way.  Any help is appreciated.

I would be interested to know if this is possible too.

There are two ways I've used to address this, one is to move the vertexes of the edge by opposing numerical amounts and constraining to an axis; the other is to rotate the edge and use constrained scaling to realign the distorted edges.

Both ways work but are not ideal solutions and are difficult to enact in some situations.