Sounds like you have a good handle on the math.
3200 is a LOT of cargo, especially if you're not full timing. I doubt two of you will approach that unless you're traveling brick salesman. That being said, it's nice to know you will be within your limits.
If you can afford it both dollars wise and tongue weight wise the PP hitch would be great.....but could be overkill. Light tongue weights are the cause of sway, sounds like with only two people you'll be able to run 15% tongue weight which should make it tow real stable (I tow a 30 ft at 12% without any issues). That being said the PP will eliminate sway, not mask it or control it like my equalizer 4 or does. The ONLY problem I've heard of with the PP is the inability for some service shops to move your rig around since there's not a traditional ball.
You could always try a $500 option like the EQ4 or Blue Ox and if it isn't any good you should be able to get $300 plus selling it used.
Keep in mind not all center of gravity is created equal, you want as much weight over the trailer axles as possible, while maintaining 10-15% tongue weight, opposed to a bunch of weight up front and then counteracting it with weight in the back. That will make controlling the sway or porposing harder to stop once it starts.
The propane will add about 90 lbs to your tongue weight (30 lb bottles or 50 lbs full, each) and a 31 series battery about 60 lbs. So that's about 150 lbs on top of the manufacturers stated tongue weight, or 850 in your case....about 13.5% tongue weight. That being said, get it weighed after you buy it. But it should be a great match with your truck. But no matter what you're pulling it with, you want it properly loaded, leveled, and balanced whether your towing it with an SUV or a full ton dually.
Hope this helps!
2016 Sunset Trail 270BH-Toyota Sequoia