Thank you all who responded with constructive suggestions. Apart from learning a great deal about perl internals, I like the result so much that I figured I'll share it with you. Criticism always welcome!
The goal was to seamlessly integrate OO exception handling with minimal effort from the user, and make the object smart enough to preserve as much information as possible along the way.

What this module can do:

• Exports a subroutine die() which throws an objectified exception.
• Performs minimal changes to Carp.pm by redefining croak() and confess(), making them throw objects. The nature of croak() is preserved, and it still reports errors from the callers perspective. A symbol table walk is performed in order to find all references to croak() and confess(), in case this module is loaded after some other modules used Carp.
• Defines a UNIVERSAL::die method, which throws an object containing a reference to the calling object.
• The object is implemented as an array representing the exception stack. Thus the following:

  eval {
      eval {
          Module::stuff(...);   # this throws an exception
      }
      croak ($@, 'More info');
  }
  die;
  [download]

  will resut in $@ containing an object with 3 frames, each containing all information pertaining to the specific exception.
• The exception object has proper stringification, based on information found in the first (deepest) frame, and formatted accordingly to the exception type (die, croak, confess, etc.) A stringification of a more recent frame can be obtained by $@->stringify ($frameno)
• Every exception frame contains a full trace produced by Carp::longmess, and exception objects have a crude ->dump() method, allowing to examine their internal state.

The Module

# package name can be anything, __PACKAGE__ is used throughout the mod
+ule
# subclassing is impractical and not implemented
package PRD::Error;

use warnings;
use strict;
use Carp qw//;
use Data::Dumper;
use base qw/Exporter/;  # probably should write my own import()
our @EXPORT = qw/die/;  # and have :objectify as a flag to objectify C
+arp
use overload (
    q/""/ => \&stringify,
    fallback => 1,
);

# this die() will be imported into any package that uses us
sub die (@) {

    # find the first caller outside of this package
    my $fr = 0;
    while (caller($fr) and __PACKAGE__ eq caller($fr)) {
        $fr++;
    }
    my @caller = caller($fr);

    my $eframe = {
        file => $caller[1],
        line => $caller[2],
        caller => 'die',
    };

    my @err;

    if (@_) {
        #check for a pseudo-object created by UNIVERSAL::die
        #(recognized by being a hash instead of an array)
        if (ref $_[0] eq __PACKAGE__ and UNIVERSAL::isa ($_[0], 'HASH'
+) ) {
            my $pseudo = shift;
            for (keys %$pseudo) {
                if ($_ eq 'error') {
                    @err = @{$pseudo->{$_}};
                }
                else {
                    $eframe->{$_} = $pseudo->{$_};
                }
            }
        }

        #check if we are called as a class method (package->die ())
        elsif ($caller[0] eq $_[0] and (@_ > 1 or $@) ) {
            $eframe->{class} = shift;
            $eframe->{caller} = 'class';
        }
    }

    # either remaining @_ or $@ or nothing
    unless (@err) {
        @err = @_ ? @_ : ($@ || () );
    }

    my $eobj = [];
    # check if this is a re-thrown error object
    if (ref $err[0] eq __PACKAGE__) {
        $eobj = shift @err;
    }

    $eframe->{trace} ||= _trace (@err);
    if (@err) {
        $eframe->{error} = \@err;
    }

    push @$eobj, $eframe;
    CORE::die bless ($eobj, __PACKAGE__);
}

# teach objects how to die
sub UNIVERSAL::die {
    my $obj = shift;

        # native object
    if (ref $obj eq __PACKAGE__) {
        &die ($obj, @_);
    }

    # foreign object
    else {
        my $pseudo = {
            caller => 'object',
            object => $obj,
            trace => _trace (@_),
        };
        $pseudo->{error} = [ @_ ] if @_;
        &die (bless $pseudo, __PACKAGE__);
    }
}

sub stringify {
    my $self = shift;
    my $fr = shift || 0;

    # no stringification when called by _trace()
    return $self if (caller(1) and (caller(1))[3] eq __PACKAGE__ . '::
+_trace');

    unless ($self->[$fr]) {
        CORE::die Carp::shortmess ( sprintf (
            "Frame index '%s' requested from object with %d frames",
            $fr,
            scalar @$self,
        ));
    }

    my $err = ( $self->[$fr]{error} )
        ? join '; ', @{$self->[$fr]{error}}
        : '';

    if ($err !~ /\n$/
            or
        grep { $self->[$fr]{caller} eq $_ } qw/confess croak/
    ) {
        $err .= " at $self->[$fr]{file} line $self->[$fr]{line}.\n";
    }

    if ($self->[$fr]{caller} eq 'confess') {
        $err .= join "\n", (
            map { "\t$_" } (splice @{$self->[$fr]{trace}}, 1),
            '',
        );
    }

    return $err;
}

# dumper shortcut
sub dump {
    my $self = shift;
    return Dumper [ @$self ];
}

# objectify Carp.pm exceptions globally
{
    no warnings qw/redefine/;
    no strict qw/refs/;

    my %redef = (
        croak => sub {
            my $pseudo = {
                error => [ @_ ],
                caller => 'croak',
                trace => _trace (@_),
            };
            {
                local $Carp::CarpLevel = 1;
                ($pseudo->{file}, $pseudo->{line}) =
                    Carp::shortmess ('') =~ /^ \s at \s (.+) \s line \
+s (\d+)/x;
            }
            &die (bless $pseudo, __PACKAGE__);
        },
        confess => sub {
            my $pseudo = {
                error => [ @_ ],
                caller => 'confess',
                trace => _trace (@_),
            };
            &die (bless $pseudo, __PACKAGE__);
        },
    );

    _redef();
    sub _redef {
        my $parent = shift || '::';
        for my $ns (grep /^\w+::/, keys %{$parent}) {
            $ns = $parent . $ns;
            _redef($ns) unless $ns eq '::main::';
            for my $sub (keys %redef) {
                *{$ns . $sub} = $redef{$sub} if (exists ${$ns}{$sub});
            }
        }
    }
}

# separate Carp::longmess into logical lines
sub _trace {
    local $Carp::CarpLevel = 1;
    my @trace;
    my $mess = Carp::longmess (join '; ', @_);
    while ($mess =~ /\s* (.+? \s at \s [^\n]+? \s line \s \d+) \s*\n/x
+mgs) {
        push @trace, $1;
    }
    return \@trace;
}

1;
[download]

Update: Fix stringification problems.
Update2: Fix the fix :)

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