3.73 gears would have been better than 3.42. 3.42 may give a little better mileage not towing but the taller 3.73 will get the load moving better and keep the rpm's in the power band of the engine when under load.
You are pulling quite a load, the shape of it is a wind sail so you are fighting the weight and the wind drag. A 1/2 ton gas tow vehicle is not going to move it at highway speed without some strain, the engine is going to rev and use a lot of gas, and sometimes you are just going to have to settle with going slower.
3 rows of seats will require as Go Dogs stated a one ton passenger van, another possibility is a good used if you can find it diesel Excursion or a Suburban 2500 with at least the 6.0 and 3.73 or lower gears.
Maybe a gear change on what you have, making sure it has the factory tow package with the larger radiator and transmission cooler and that the cooling system is clear of any mineral deposits and has the right mixture of fresh coolant.
I went from towing a 28 foot travel trailer that was close to 6000 pounds with a 1/2 ton 5.3 Suburban to the F250 with the diesel. The Suburban got it moving but did take a lot of gas and on hills it was in second gear revving high if I wanted to maintain speed. I could have gotten by with it but at the time could afford to upgrade my 1/2 ton truck so I bought the diesel.
I could have kept going with what I had and went slower since most of my travels at the time were in the south in the flat part of the area.
Take a break, look at your options before spending any more money and make sure what you spend gives you the most bang for you dollar.
If the current vehicle tows stable without sway and power is you only issue there are things you can do to make slight improvements without breaking the bank. The least expensive is a gear change and probably a computer flash to up the shift points when towing and let a little more hp and torque out.
Are there any performance 4x4 truck shops or speed shops in your area? One of those could offer you some solutions that will help but not so much power that you are breaking things in the driveline.
