Since Pod::Classdoc just uses special POD tags ("=begin/end classdoc") wrapped inside POD sections, presumably its just a matter of writing an appropriate POD filter (plus something - e.g., PPI - to detect the beginning of package/method definitions).

OTOH, maybe Lynx would work with the HTML version ? I've not tried it (and frankly am not inclined to).

BTW: thanks for the NaturalDocs link, I'd not heard of it before.