I want to add a stratopan repository to the list of mirrors cpanminus uses on a machine.

stratopan ? hum, new to me :) Private CPAN in the Cloud - Stratopan

I don't want to have to specify the mirror with the --mirror command each time.

Call your program cpanmm and have it specify --mirror each time :)

I have set PERL_CPANM_OPT to "https://mymirror"

Um, you mean "--mirror=https://mymirror" right?

but cpanm only looks for dependencies on my mirror, and not the default repository. How do I make sure cpanminus looks in the default repositories if a module is not found in my repository?

um, try cpanm --mirror https://mymirror --mirror http://www.cpan.org ...