The VA override will make that operator *always* used everywhere.
If you want to use a different logo for an existing operator, and keeping the same assignment, the only way is to replace the actual .DDS texture, but this will be overridden by GSX during a Live Update.
I suggest waiting for the next GSX update, which will change entirely the way you do custom operators, making way easier and more flexible. Under P3D4 only, of course.