You've got the same Jeep and year that I have.
I also have a car hauler and wouldn't dream of using it to haul the jeep. Towing four down is very convenient. DW helps me to disconnect it and it might take four minutes to disconnect and drive it away. We love it.
I have a Unified Tow Brake system and don't know how a Brake Buddy might differ.
Given your massive trailer, I'm not sure how it would feel to down size the space available for hauling stuff.
But I gotta' tell ya', the convenience of easy disconnect and ability to easily explore surrounding campsite areas is exceptional.
