Found this on Budget's T&Cs
3.1 You and any Authorised Driver must only use the Vehicle on a road, which is properly formed and constructed as a sealed, metalled or gravel road.
I'd take that to mean some dirt roads as long as they're built like a road. The next line (and there's something like this in all the ones I looked at) says
3.2 You and any Authorised Driver must not, unless authorised in writing by Budget, drive or take the Vehicle: blah blah
So maybe try calling up one of the companies, tell them exactly where you want to go? Maybe you'll be able to get a written authorisation for it? Or at the very least they might say "yes that will be fine, but you'll have to hire the LandCruiser" or something like that.
Worth a try methinks