Instead of pushing each $line onto @allmembers as its own element, you could chomp the @members array then join the contents of @members into a string. Pushing this string onto @allmembers should then be what you want...

foreach my $member ( .... ) {
   ....
  close(FILE);

  chomp @members;
  my $bigline = join(' ',@members);
  push(@allmembers,$bigline);
  ....
}

for my $longline (@allmembers) {
  print "$longline\n";
}
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Update added my to original foreach loop var per tilly's wise words.

-Blake