I'm not aware of a CPAN module that does what you want, but if you put something like

=for BASE_METHODS_START

...

=for BASE_METHODS_END
[download]

into the POD of the subclass and then use a script that parses the base class(es), extracts the method POD pieces from them and then plunks them down in the subclass POD with a substitution like

$data =~ 
  s/=for\sBASE_METHODS_START.*?
    =for\sBASE_METHODS_END
   /=for\sBASE_METHODS_START\n\n$otherpod\n\n=for BASE_METHODS_END/xgs
+;
[download]

then you should be good to go.

This script in the distribution of Perl::Configure uses this trick to add a dynamically generated ascii table into the main POD.