There isn’t a need to create a lighter unit to get them from ship to shore. The amphib task force has to operate ashore like any other unit and they need the same things as the others. Arguably they need more combat power than other brigades because they are the spearhead. Also the limitations on the LHDs are not weight but density. So heavier combat assets like tanks and SPGs provide a lot more combat power per square meter of garage space than gun buggies and towed artillery.Or the 4th Brigade could be an amphibious one with a lighter footprint.
2 Sqn with Amphibious Vehicles (+ maybe another one with Bushmaster)
2 Infantry Battalions
2 Arty Batteries+
1 strengthened Engineer Coy
1 Support BN with Beachmaster units and other units necessary for amphibious ops.
You would need fewer vehicles and men, and could consequently adapt to amphibious warfare.
If 2 RAR BG was expanded to an amphibious brigade it like 2 RAR should be structured as per the other brigades and battlegroups. There is of course a case for equipping the APC squadron with an Amtrac and adding co-locating with a 10 FSB type unit for amphibious logistics support capability.