Indeed, this problem is not really solvable. However, my solution does offer a partial way forward.

Let's imagine that My::AwesomeError and Your::GroovyError both superclass Example::Error, and both add an asplode method.

We can then do:

my $err = Example::Error->new('Heat death of universe detected!');
$err->My::AwesomeError::asplode();
$err->Your::GroovyError::asplode();
$err->asplode();  # Russian roulette
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With true monkey patching, where My::AwesomeError and Your::GroovyError each defined the asplode method directly in the Example::Error namespace, we wouldn't get the option to do the above.