Okay, so I think I may have figured this out.
Right before the Sub Report prints, there is a Report Footer section that gives the grand totals for the report. So I initialized a global number var on the Report Header that is equal to 1. When the Report Footer comes around I equaled it to 0. I have the Page Header suppressing if the global number var is less than 1.
This works for now. If anybody sees some flawed logic in this, please chime in, but for now, I'm keeping it like this.