just a little more power

The 2015 Super Duty 6.2 came with either a 3.73 or 4.30 rear end. If the OP’s is 3.73 the Ford tow rating for the 3.73 is 12,100. With the family and the trailer loaded up the OP is likely close. The rear end ratio was important back in the 3 or 4 speed transmission days because the gear ratios were far apart. The 6 speed in a 2015 has much closer ratios—just let it shift. Valhalla360 has the right idea. Acceleration and mountain pulling are all about HP because HP has RPM in the equation. The exact equation is HP = Torque x RPM / 5252. The 6.2 is an overhead cam engine that will spin up to 5000 RPM although you might not want to listen to the noise. If you want to go faster push the accelerator. Also, changing the rear end ratio involves two gear changes because of the 4x4—not worth the cost. My son has the same truck in a 2012. He pulls upwards of 10,000 lbs of livestock or 12,000 lbs of hay. It never runs in 6th pulling a trailer on level ground. As stated above gas engines just don’t put out much torque at low RPMs. Using the formula: less torque = less HP at any given RPM. The best gas engine (without turbo) for low end torque is the Ford 7.3 available in 2020 or later.