It would be nice to be able to choose a new reference for selected viewports. That would be a good feature request. In the meantime, the method I describe and which Charlie uses works fine and is easy to do.
A quick example following the description of the OP’s setup.
Four SketchUp files representing four different schemes. Each scheme has five scenes.
In LayOut, document started using Scheme A model. Viewports distributed on page as needed. Note: It is critical that the scenes not be modified in LayOut.
File saved and named, of course. Then a copy is saved with Save as… and a new name. In this case, saved as “Scheme”.
Relink the SKP file to Scheme B.
Copy the viewports and paste on a new page in the original document.Repeat for each of the other schemes. No need to create different documents for each scheme. When finished, each page will show a separate scheme and all of the viewports will be lined up just as the OP requested. Just use the same “Scheme” file for each additional scheme.