IMHO the already described technique of monkeypatching wrappers is the best general approach, it's also easily reservable with localized *globs.

Concerning this special tracing Perl offers various approaches for that, like activating it in debugger-context.

It should also be possible to tweak Carp to adjust intendation or to use an alternative Carp from CPAN.

Changing your classes for that special need only looks like overkill to me and smells a lot like an XY Problem.