Found a solution that works for this document at least. I removed all of the field codes with Alt + Shift + F9, and now the user can print the document without triggering the error noted above.

What led me to this solution was another thread; I could not fully understand the OP's reasoning for the solution, but it gave me the idea of removing my cross-referenced table and figure callouts. I had abandoned using table and figure referencing years ago. Perhaps this was one of the reasons why.

So I suppose that a better solution would be to figure out which of the cross references were causing the issue, as I imagine it was not all of them given that only certain sections were affected. That way we could retain the cross referencing (as of course it is useful to readers of electronic documents, especially long documents), but for now it will have to do.