@joshkeller I just did all this research myself recently for my 3.0 Auto truck with a 4.10 rear end. I went with a 205/70R16 touring/highway all season. I've seen better coasting, and slight improvements in fuel economy when compared to a just barely wider winter tire setup.
Upping the tire height diameter CAN sometimes improve mileage if it puts your RPMs in a better range at cruising speed. You'll have to do some math to figure out if upsizing the tire diameter is worth it for you. It will make your truck accelerate even slower however.
The best choice for fuel economy (in my opinion):
Overall, the best benefit you'll see will be from reducing the tire's width, and selecting a tread that's lowing rolling resistance. If you can find affordable 16 wheels that are 6.5 inches wide or lower, then I would recommend purchasing 195/75r16 tires. These are found on commercial vans, and typically have a 105/107 Load Index rating meaning you can load up your truck, tow, and be in a safe range, while still having the thinnest possible tire. These tires are very thin a 7.7 inches wide when compared to the stock 8.8 inches from a 225/70r15, but still support a lot of weight.
The other best thing you can do in regards to wheels and tires is to go for a lighter wheel, alloys will save you some weight over steelies and help with towing, overall fuel efficiency, and performance. Since you do haul, even though its not the heaviest, make sure you buy quality alloy wheels, or OEM alloys.
My recommendation for you:
In your situation and with your current 15inch wheels, I would recommend either sticking with 225/70r15s, or down sizing to either 205/75r15, or 215/70r15. You will get just over 1% reduction in tire height on both, and a reduction of 0.8, or 0.4 inches in width respectively.
Overall, you're not going to see a remarkable improvement in fuel economy, but you may see some, if you need new tires then I'd recommend going smaller, if you don't need new tires, save yourself the money to buy gas.
EDIT: Read your other posts a bit more closely, ALL of the tires I mentioned should give you some sort of fuel economy benefit compared to those 235/75r15 tires you have.
Since you're looking to get new tires, if you also want to buy wheels, then i'd go for the 195s, if you want to keep your existing wheels, then 205/75r15 is my recommendation, but you'll see some improvement by just getting new 225s as well, they're also a lot more common.