The reason I ended up using the Green BG (and will likely be using it in the future on certain units) is that when you have a unit with bright-red items/accessories, there is a tendency for the brighter shades of Red to be mistaken for some of the BG color by my paint program when it applies the palette, so I ended up with pinkish spots on the sword and her tights... By simply re-mapping the shadow colors (all I did was go into the PaintShop Pro palette editing tool and set the "hue" to, IIRC, 83) to green, and re-rendering with a suitably green BG, I was able to completely eliminate the problem... I also ended up using this technique with my General Beatrix unit and at least one other as of yet unreleased unit that I made recently to solve palette issues.
In the future, if I end up doing a unit that has a lot of red (or maybe even one that uses Red as its civ-coloring), I'm going to set the BG to straight Green (RGB = 0,255,0) from the get-go so I don't end up having to re-render the entire unit after finding palette bugs when rendering on a magenta BG.