I looked at the perldoc and pod2man man pages and it was not clear to me as to how to make perldoc ignore the POD embedded inside the heredoc. How can I do that?

I'm not aware of any way to do so. Creating a parser that could ignore POD in quoted text would require a way to recognize quoted text, which would require parsing Perl source. Even if one succeeded in such an effort, it would only work for tools that used it. Syntax highlighting in most text editors would still barf, as would most any other POD-aware tool. I personally wouldn't want to maintain a source file with two or more sets of POD in it, either.

What I would suggest is to store the POD file as an external template and use Text::Template for easy flexible interpolation.