Suppose you look at a bunkhouse TT under 4500 lb dry (advertised dry weight) it will probably wind up weighing closer to 5000 lb dry with real world options plus LP tanks and battery. Then add your cargo and maybe a little bit of water (not much!), and you're around 5500 lbs, maybe more. That's about 600-700 lbs on the hitch, if it's all balanced correctly. Then add almost 100 lbs of the weight distributing hitch with some sway control. Nope, not enough payload.
There are a few super-light TTs that could work, but those tend to be single axle, small, low cargo capacity units. For example, KZ Sportsmen Classic 180BH. You might wind up with a real world hitch weight of 500 lbs or less.
