When you mix Portrait and Landscape in a document, the Landscape page comes
out with the top to the right, I assume so that automatic staplers can staple
it in the upper-right corner (which is upper-left if you rotate the page to
Landscape). But in most manuscript material, you want the top to the left,
or inside if the pages are single-spaced and bound or stapled on the left.
Any way to tell Word or the printer to flip the page upside down?

Not from within Word. Some printer drivers allow you to choose
the rotation direction when switching from portrait to landscape.
Look around in File-Print-Properties to see if your printer
gives you such an option.

Allan Editor wrote:

When you mix Portrait and Landscape in a document, the Landscape page comes
out with the top to the right, I assume so that automatic staplers can staple
it in the upper-right corner (which is upper-left if you rotate the page to
Landscape). But in most manuscript material, you want the top to the left,
or inside if the pages are single-spaced and bound or stapled on the left.
Any way to tell Word or the printer to flip the page upside down?