... this seems such a simple thing to be able to do, not even a majorly complex problem.

It is simple, but there's nothing so simple that it cannot be made more complex. :)

IIUC, you're not using package anywhere, so all your code is in the default main package. But for some reason you can't use the fully-qualified $main::variable_name (with $ replaced by the appropriate sigil) form to access globals, nor can you use
    our $variable_name;
statements to declare variables within the file-scopes of the various source files of your application.

I think you're right: avoid strict and warnings like the plague, and use the unqualified form for all globals. If nothing else, it will be employment insurance.