Any ideas?

As it happens, yes. Note that   m#</div></div># will not match

  </div>
  </div>
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because there's (vertical) whitespace between the two tags. You need \s* in your regex at points where whitespace is expected to appear between tags. And you need to slurp the entire file into memory first, since doing this line-by-line won't work.

I've not tried it, but perlrun notes that -00 will force Perl into "paragraph" mode. Given your HTML, that might be sufficient. Otherwise, investigate the other options in perlrun.