I've been through the Bungles on a push bike - so that's a thing, but yeah, Cape Peron would be a hard slog without a boat or vehicle that can push across deep sand - water would be a tough carry.
> without the right vehicle
A loong time ago (late 1970s) I got to traverse the horizontal falls a couple of time in a home made sea kayak after being dropped off "nearby" (and later picked up again) by an old pearling lugger .. pretty low carbon effort that one, just a lot of paddling (and fishing, and digging for fresh water, and dodging the odd shark and salty croc).