I rented a Ram Promaster city from Enterprise in Kona
It was cheaper than the cheapest rental car from the airport.
I slept in the back some nights and in a tent others for 7 days.
I packed my camp stove, tent, utensils, and other essentials in a cooler as a luggage item.
With a quick stop by Home Depot for precut plywood and a screw gun you could build a platform in the back two people can sleep on and stow gear underneath.
It got me where I wanted to go off road.
I didn't see any "4x4 campervans" for rent there.
The Big Island is awesome, this is a great way to see it.