Some of the battery/LP weight will be borne by the TT, but you'll probably still be around 600 lbs hitch weight. If the water tank is up front, you'll have to run fairly empty on water. The JGC rear end and receiver should stand up to over 700 lbs hitch weight IIRC, since I am pretty sure it's all the same whether the engine is V6, V8 or ecodiesel. You'll be close and will have to do some weighing to make sure you don't exceed that, but it should be do-able.
I always thought the Equal-i-zer worked well for me and was easy to self-install. It won't save you any weight, though. Just another option.
If you replace tires to gain stiffer sidewalls, consider a size or two smaller for lower profile; this can reduce the tire's ability to squirm side to side under pressure.
