...and $? is zero, so I can't get a return code.

close waits for the subprocess and sets $?:

my $pid = open X, '-|', 'echo foo; exit 42' or die $!;
my $out = <X>;
my $ok = close X;

print  STDERR "out=$out";
printf STDERR "\$?=%s\n", $? >> 8 unless $ok;

__END__
out=foo
$?=42
[download]

See close for details.