Sorry I can't help with your exact LWP problem, but is there a reason why you're querying the Web UI of the 3300?
From experience SNMP is a much better way of obtaining information from networking equipment. Generally the mac address database/FDB is in the same place in the tree, however you could just look up the manufacturer's OID to find it and query that using Net::SNMP
I know some networks groups get a bit twitchy (well, mine does at least!) about SNMP so maybe it's not a solution for you :(