I finally found an acceptable workaround for the formatting I want. I moved the repeating header information out of the Page Header and into a separate grouping that is a child to the return address information group level and a parent to the grouping that contains the rest of the data. It is a compromise design, because the other arrangement is definitely preferred, but at least it can work.

What I have learned from this is that you should not rely on any method of putting dataset data into the Page Header or Page Footer. There is a bug that will, under some circumstances, put the wrong data up there. Maybe it is just the complexity of this statement's report design that is making is susceptible to the bug, but now that I know it exists, I am unwilling to risk running into it again in any report design.