My thanks to all who offered advice. Here is the solution now put into practice (most of the irrelevant code omitted). Note I had to use a homegrown alternative to FileHandle because its documentation didn't mention support of Open3. That was just an array of self-numbering filehandles for easy deletion.

package jiloader;

use Parallel::ForkManager;
use IPC::Open3;
use Fcntl qw(:flock SEEK_END);

sub new {
...
        $opt { MAXFORKS } ||= 31;
        $opt{ PM } = new Parallel::ForkManager( $opt{ MAXFORKS } );

        $opt{ PMFH } = []; # filehandle pool
...
        # example of one of four files that track things
        unlink $opt{REJFILE};
        open my $rejh, ">>$opt{REJFILE}"
          or die "$!: $opt{REJFILE}\n";
        $opt{ REJH } = $rejh;
...
        bless \%opt;
}

...


sub put {
        # batch changes by outer box
        # for submission to fork scheduler

        my $self = shift;

        if ( $self -> { REST } ) {
                if ( $self -> { TOPBOX } ) {
                        $self -> { BATCH } and $self -> sched;
                }
                $self -> { BATCH } .= $self -> { CHG };
        }
        else {
                $self -> { BATCH } .= $self -> { CHG };
                $self -> sched;
        }
}
sub sched {
        my $self = shift;
        my $pm = $self -> { PM };

        my $rh = $self -> getfh;
        my $wh = $self -> getfh;
        my $eh = $self -> getfh;

        # parent has allocated fh's so has to
        # free them when child exits
        # child cannot do this whatever the fh pooling solution

        $pm -> run_on_finish( sub { $self -> killfh( $rh, $wh, $eh ); 
+} );

        unless( $pm -> start ) {

                open3 $wh, $rh, $eh,  $self -> { JILCOMMAND };
                print $wh $self -> { BATCH };
                close $wh;
                unless ( $self -> jiloutparse( $rh, $eh ) ) {
                        my $errh = $self -> { ERRH };
                        flock $self -> { ERRFILE }, LOCK_EX;
                        print $errh $self -> { LASTOUT };
                        print $errh $self -> { LASTERR };
                        flock $self -> { ERRFILE }, LOCK_UN
                }
                close $rh;
                close $eh;
                $pm -> finish;
        }
        $self -> { BATCH } = '';

}
...
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