Unfortunately, there appear to be few Visio users on this forum and I'm a long way off being an expert in it myself.

I had a play with the backgrounds and can see your issue but it doesn't appear to be an insurmountable problem to me. Is it such a great issue to create backgrounds with Portrait and Landscape variants and apply the right one according to the page setup?

I did find another thread which seems related to this question and it looks like they used code to modify the position of 'background' objects related to the page setup. They were doing this in earlier versions of Visio so perhaps this isn't relevant to your experience with background pages.
Background Size

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Andrew Lockton
Chrysalis Design, Melbourne Australia