my $ua = LWP::UserAgent->new (max_size => 512); # note extra param

my $tmpfile;
foreach my $rev ("-", ('A'..'Z')) {
  $tmpfile = "$file$rev.$ext";
  my $response = $ua->get("$path/$tmpfile"); # simpler interface
  ## you need to save $tmpfile here!
  last if $response->is_success; # better than yours
}