We use this Camp Chef Ranger 2-burner stove with regulator removed that hooks into our camper propane with a quick connect. https://www.campchef.com/ranger-ii.html.
Cranks heat and stays clean. It lives in our generator compartment.
With it we use a griddle such as this: https://www.amazon.com/Nordic-Ware-Burner-Backsplash-Griddle/dp/B0089XJDP8/ref=sr_1_32?dchild=1&keywords=non-stick+griddle&qid=1592699952&sr=8-32
It is very versatile from pancakes to veggies to steaks. We used to have a Weber Q grill, but it was so bulky and HEAVY to store and MESSY and smelly in the camper. Our current setup is much more user friendly. Only thing you miss is the flame-grilled taste.
We never had a front to back porpoising issue but we recommend upper stable loads and Timbrens. We have them on the duallys. No sway side to side. Rougher ride over big bumps when camper is off truck.
Propane use sounds excessive. We don't leave the hot water heater on 24/7, only takes 15 mins or so to get the tank hot when needed.
Hint on showering: Turn heater on for about 15 mins then turn it off. Now take your shower with only the hot water knob on. No fiddling with hot/cold mix and wasting water. For a second shower right after, turn water heater on for an additional 4 mins or so and the next person is set. This seems to work for us just fine, your heating times may vary, also depending on outside temp.
2014 Ram 3500 CrewCab Diesel DRW 4x4 4.10 Aisin, Torklift Fastguns, Upper Stableloads, Timbrens
2017 Northstar 12' STC
640W solar, 400Ah lithium LiFeMnPO4 batteries