None of the suggestions have worked, but I found a solution. In my VRML.pm file, in any subroutine printing output, I added a myprint argument and where the subroutine originally invoked &printout, I changed it to invoke \&myprint, where @lines is an array of lines to be printed:

sub egg { # prints a 3d egg.
 my %args=(myprint => \&printout, xaxis => 10, ...);
 # Produces lines of wrl output in @lines ...
 $myprint=$args{myprint};
 &{$myprint}(\@lines);
}
[download]

In DrillPressTable.pl, which uses VRML.pm, I added a global $Fh, and changed the invocation of mystart, and its code, and myprint's code as well:

my $Fh; # w/b set in mystart.
&mystart($LumberFile,LF);
sub mystart {
 my($file,$fh)=@_;
 open($fh,"> $file")
  || die("ERROR: Unable to open $file for output");
 $Fh=$fh;
 my @lines=split(/\n/,<<END);
#VRML V2.0 utf8
NavigationInfo { headlight TRUE }
...
END
 &myprint(\@lines);
}

sub myprint {
  my($lines)=@_;
  foreach my $line (@{$lines}) {
    print $Fh "$line\n";
  }
}
[download]

So now in DrillPressTable.pl I can direct lines of output to multiple file handles, and I don't need to change any of the 70-odd perl programs that use my VRML.pm. They'll just take the default of &printout, which prints to STDOUT, just like before.