I reckon the baitcaster on that rod with 30lb braid will be fine. My reference to budget was just that. My favourite barra setup cost about $800 and is probably a bit lighter,smoother and more durable but that setup you're looking at will catch any barra in lakefield. I would use it over those other options you mentioned.
Of recent times I've been collecting old baitcasters and I always try and get a few barra on each one before putting it on the shelf. The pic in my avatar is an old 2 speed shimano bantam on a 72cm barra caught in Lakefield, off the bank. It doesn't have instant anti reverse and is a bit clunky but casts well and the drag is smooth.
You can catch a barra on any gear. Price just makes it nicer to use.
Like Nagg said, If a big barra plays dirty it doesn't matter what gear you're using, particularly from the bank.
Just use a decent length of 60lb leader tied with a knot that won't catch on the levelwind or guides when casting (suggest fg knot). That way you'll be able to drag most fish out of the water without getting eaten.