In case anyone else is looking for a way to convert Crypt::RSA keys, or for a way to generate an RSA key given its integer elements, here is the solution I eventually came up with:

use Crypt::RSA;
use Crypt::OpenSSL::RSA;
use Crypt::OpenSSL::Bignum;

$key = new Crypt::RSA::Key::Private (
                                     Filename => 'private.key'
                                     Password => 'secret-word'
                                     );

$n =  Crypt::OpenSSL::Bignum->new_from_decimal($key->{private}->{_n});
$e =  Crypt::OpenSSL::Bignum->new_from_decimal($key->{private}->{_e});
$d =  Crypt::OpenSSL::Bignum->new_from_decimal($key->{private}->{_d});
$p =  Crypt::OpenSSL::Bignum->new_from_decimal($key->{private}->{_p});
$q =  Crypt::OpenSSL::Bignum->new_from_decimal($key->{private}->{_q});

$rsa = Crypt::OpenSSL::RSA->new_key_from_parameters($n, $e, $d, $p, $q
+);

print $rsa->get_private_key_string();
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