open my $output_fh, '>', \my $mime_body
    or die "In-memory handles are not supported by your version of Perl.";
$mime->print( $output_fh );
close $output_fh;
$mime_body =~ s!\n!\r\n!g;
# use $mime_body as the string wherever you would use it with SOAP::Packager
# I don't know if the following is valid, using a raw string as a MIME part:
$soap->parts( [$mime_body] );