I decided my multiple Perl installations were probably to blame for these issues and I'm going to bite the bullet and uninstall all Perls on this computer and start from scratch with Strawberry, after I've run one more key script.

Strawberry has an uninstaller, which tells me, helpfully, that uninstall is complete, but that some components haven't been uninstalled, that they can be uninstalled manually, but not what they are.