CPAN clients do a "static" parse (really a single line execution) to check the installed version of a module.

That's interesting and certainly news to me (++). I take it you mean that they do something like a grep for '\$VERSION\s*=' and then execute that line/statement in isolation? It's obvious how that would fail for anything but the simplest cases. Is this documented anywhere?

With your knowledge of these clients, is there any solution to maintaining a uniform version number across multiple modules in a single dist other than just brute-force updates of static scalar values?

Update: To answer my own question, see https://metacpan.org/pod/distribution/ExtUtils-MakeMaker/lib/ExtUtils/MakeMaker/FAQ.pod#Generating-*.pm-files-with-substitutions-eg-of-$VERSION which has a solid-looking answer, if not perhaps the most elegant. I will have a play with this but it looks like it might be a winner.