One option is to generate a separate print job for each member in a loop instead of printing the found set using the records being browsed option.
Another option might be to use save As PDF to build and then open for printing a PDF file of your report. This can also be done in a loop where the last layout is a separate save as PDF and the append option is used to combine the many different reports into a single file. The main limitation here is that the final, conditional layout has to start on a new page when you use this option.
Oh! Somehow I had missed the Append option in PDF generation.
Having to start a new page shouldn't be a problem since, as I mentioned, the dynamic portion of the layout is on its own page anyway.
I'll investigate this and report back as to how it turns out.
Append did the trick.