I'd suggest using XPath for that; this is exactly the sort of thing it was made for. There's a decent module on CPAN, XML::XPath; here's the XPath spec (and a newer one that came out while I wasn't looking, apparently), and here's a tutorial introducing and discussing XPaht selector syntax.

This approach may not work if your HTML isn't well-formed, though; in your example, for instance, there's no </ul> tags.