Thank you Anonymous Monk! I did need to change it a bit to make it work as I was having issues getting the headers information and things appear to working rather nicely now.

For future reference, and in case others find it useful, the modified send_file is:

    return send_file(
        \'fake contents to be replaced in override',
        streaming => 1,
        callbacks => {
            override => sub {
eval {
    my ( $respond, $response ) = @_;
    require LWP;
    my $ua = LWP::UserAgent->new;
    my $writer ;

    $ua->get(
        $new_route,
        ':content_cb' => sub {
            my ( $data, $response, $protocol ) = @_;

            if(not $writer ){
                my $h = $response->headers ;
                my %m = map {$_ => $h->header($_)} 
                    ('Content-Length', 'Content-Type', 'Last-Modified'
+);
                $writer = $respond->( [ $response->code, [ %m ] ] );
            }

            $writer->write( $data );
        }, ## end of :content_cb
    ); ## end of $ua->get
} or Dancer::Logger::error("stream-file: bad eval $@");

                return;
            }, ## end of override
        },
    ); ## end of send_file
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