Can you not simply redirect STDERR / STDOUT?
This example (from the camel i think) redirects errors into a FH and to stdout. so you still get them on screen and in a logfile. You would only then need to rediirect STDOUT as shown above?

sub make_log{
    # make a log file 
        my $log = shift;
    
    # open the log and stamp it
    open (my $log_file, '>>', $log) || die "Failed to open $log:\n$!";
    print $log_file "\n------> log for $0\n------> ".scalar(localtime)
+."\n\n";
    
    # make sure errors are put into the logfile
    # i.e. print STDERR "weird" ~ not in logfile
    #         warn "freaky"        ~ in logfile (and the screen)
    #        die "AAaaarrrrrgh!" ~ in logfile
    $SIG{__WARN__} = sub {print $log_file @_;print STDOUT @_};
    $SIG{__DIE__} = sub {print $log_file @_;print STDOUT @_;exit 1};
    
    # return complete
    return $log_file;
}
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