You can certainly get GaussView to save 3D density data to files for you, either to reload at a later time or to manipulate externally; Gaussian calls these cube files.  GaussView will also generate the sum or difference of a cube and can square a cube.  What I have been unable to determine in a brief investigation is whether or not you can square the HOMO, save it, square the LUMO, save it, and then reload them and take the sum.  Even if you can't do this, however, it would seem fairly trivial to write a script to sum the corresponding elements of the two files and generate a new cube.  That might also be the necessary solution to the "y x" portion of your equation – is that multiplication by a scalar?  Of course, by the time you're doing that much external manipulation, you might just prefer to have GaussView output the cubes and do all the math externally, since that would be easier to debug.  Once the desired cube file is generated, you can load it back into GaussView, manipulate it in three dimensions, and generate images for publication, etc.

Odd electron density can be very easily plotted by Multiwfn (http://sobereva.com/multiwfn), there is an example given in Section 4.A.6 of the manual.

You could also use the package AIMAll (aimall.tkgristmill.com) to plot, among other things, the orbitals, net spin density, and other features of the electron density topology

Thank you Tian Lu, that worked exactly as I wanted. I was able to do everything I needed in just an afternoon.