Regarding your update, it's easier not to substitute in-place when using a parser.

sub parse_bin {
   my $save = pos;
   my ($size_sz) = /\G \# (\d)        /xgc  or goto BACKTRACK;
   my ($bin_sz)  = /\G (\d{$size_sz}) /xgc  or goto BACKTRACK;
   my ($bin)     = /\G .{$bin_sz}     /xgcs or goto BACKTRACK;
   return $bin;

BACKTRACK:
   pos = $save;
   return ();
}

my $outputText = '';
for ($inputText) {
   pos = 0;

   for (;;) {
      if (my ($bin) = parse_bin()) {
         $outputText .= '<Binary block: '.length($bin).' bytes>';
         next;
      }

      if (/\G (.[^#]+ ) /xgcs) {
         $outputText .= $1;
         next;
      }

      last;
   }
}
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Update: The parent's update was updated to generate $newstr since I started. Note that even with the update, the code doesn't behave as a regexp would. It silently drops bits of text instead of backtracking. For example, the "#" in "What you're #?" is dropped, and so is "#1" in "You're #1!".