If your trailer is 12k empty and you haul three horses and gear, you're over weight for your truck.

The Ford diesel and transmission is the same when used in both the 250 and 350 variants. The fact that you live in Durango, will have a strong bearing on the durability of your truck's drive train. One of your mountaineous trips would be equivalant to several of my mountainous excursions, and so would the drive train wear and tear. It's longevity is directly related to the usage it provides.

You can beef up the truck and enhance its performance. You can't change its total weight bearing or towing capabilities, without compromising its structural integrity. Presently you have too large a trailer for your truck, especially when considering your location and usage.

Many flat tires are often caused by under inflation, over weight conditions, mechanical axle problems or cheaply made foreign tires. It basically means that the tires are not up to handling the weights, upon which they are subjected.

Your brakes are short lived because of your high weights and extreme trailering conditions. You might consider a motor braking devise, and using your transmission's lower gears when decending the mountains. Your "million dollar highway" is a difficult challenge for any rig. It and similar roads will exact significant wear on any running gear.

Sarah, What year is your truck?

Ford has continued to improve their automatic tranmissions.  If you truck has the older 4 speed, They were prone to needing repairs. The newer 5 speed held up very well. And so far the 2011 6 speed is holding up great.

Also the earlier SuperDuties were hard on brakes. My 2000 needed the rotors turned every 36,000 to 40,000 miles because they would warp, I assume from the heat of stopping that truck and the trailers I pulled with it. In 2005 Ford increased the Brake rotor size to help solve that problem. ( Thats why the trucks went from 16" to 18" wheels to allow the room for the larger rotor) I never needed the rotors turned on my 2006 truck. So Ford seemed to have fixed the weak brakes that needed to be replaced often.  Also with the 5 speed transmission, you went from a Over Drive Lock Out on the old 4speed tranny to a Tow/Haul on the new TorqueShift 5 speed. The Tow setting kept the Torque Convertor Locked up on down hill grades when coasting so you got some engine braking to help slow the rig that wasn't available with the older 4 speed Auto.  These improvements changed my brake repairs from every 36k on the 2000 F350 to over 70k on my 2003 and 2006 trucks.

Bottom line is that if you have a 2003 and newer superduty, it's brakes will last much longer than the 1999 to 2002 Superduties, doing the same work.

My 4H Logan XT with the Platinum LQ weighs in at 16,000 loaded with horses and water. So I'm sure its right in that same weight range as your trailer.

As far as tires, on a trailer that heavy, You have no choice but to run Load Range G tires if you want to stay with a 16" tire. And Goodyear G614s are the best in that weight range. Logan has installed them as the factory installed tire for the past 4 years. If the tire problem you are having is on the truck, Step up to the next size larger to help get more capacity.

If you do look to change trucks, The F350 do offer some features over the F250. And the Brake master controller is one of those features that is improved by buying the 1 ton vs the 3/4 ton truck.

Empty 4H GN trailers weight 5000-6000 lbs.  Add the LQ and you will add another 2000-4000 lbs.

I'd really be surprised to see a 4h WITH LQ for 5500 lbs.  That weight is probably what that trailer weighed before the LQ was installed.

Rocky,  Look at your door panel and see what your truck is rated to tow.

I suspect with a 3/4 ton truck, your problem will be with pin weight in the bed. An 11,000lb trailer plus several 1000 lb horses in the back will be 13,000 to 15,000 lbs.  Pin weight is roughly 25% of total trailer weight.  13,000 lbs x 25% = 3250 lbs on the pin. And I bet your 3/4 ton truck is not set up for that much weight over the rear axle.