It returns a sort of parse tree with an array ref for each block or line, where blocks look like ['BLOCK', $name_of_block, @lines_in_this_block] and lines look like ['LINE', $key, $value].

Depending on your exact data format and what you want to extract, hashes might be more suitable.

The file is up to half a gigabyte, I'm not keeping all that in memory. I could split it up by job, I suppose.

You don't have to keep it all in memory. My parser uses just one line of lookahead, you can easily refactor the shift @lines; and $lines[0] into subs that work on a file handle.

{
   my $line = <DATA>;
   chomp $line;
   $line =~ s/^\s+//:   

   # handles '$lines[0]'
   sub peek {
       return $line;
   }
  
   # handles 'shift @lines'
   sub next_line {
       my $tmp = $line;
       $line = <DATA>;
       chomp $line;
       $lines =~ s/^\s+//;
       return $tmp;
   }

   # handles boolean check for @lines
   sub is_exhausted {
       return !defined $line
   }
}
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I didn't test it, but it should work along these lines.

Instead of nitpicking details, think on the overall architecture and fix small issues for yourself.