Not to take away from your FR, but why “of course” with different folder names? Shouldn’t it be possible to unify the folder paths across your machines and prevent these problems to begin with?
The problem with your solution 2 is imho that storing only a relative path can be counterproductive in other scenarios/workflows.
Yes, there might be a problem working with relative paths. But when I select “In the MixDown Folder” (or similar, my Cubase is set to german). This MixDown folder exist on the same level where the project is located, it’s not changeable and that’s fine. When selecting MixDown folder why is the absolute path stored in the project?