I want to set Heading 1's paragraph format to place a page break (or section
break) before the paragraph so the style places the heading on the right side
page. The left page in the verso-recto pair may or may not be blank as a
result.

I'm inclined to think this hasn't been made into a Word feature yet, but
sometimes options and work-arounds are hidden in strange places. Yes, I know
I can insert a page break or odd section break manually, but I want it as
part of the format.

Are you listening Microsoft? This would not be hard to code, and there's
plenty of space in the Paragraph format dialog box under the Line and Page
Breaks tab.