I’m really looking for a way to get an external static library compiled into a Perl module shared library. Is that even possible?

Definitely possible - in fact that's precisely what happens when you build the perl module against a *static* build of the external library. (Therein lies one reason that I prefer to build static, rather than shared, libraries.)

Your problem, as I see it, is that you want to incorporate a *shared* library into the perl module's '.so'. If that can be done, then I don't know how to do it .... it undoes what shared libraries set out to achieve, so I'm a little sceptical.

Cheers,
Rob