Tires for OEM 18" Wheels
I ran 35x12.50-18s on the stock wheels on my '05 very successfully, and on my Early 1999 with the '05+ axle and suspension swap I continue to run stock 2005 18" XLT aluminum 8-hole wheels with that size tire.
Being its a 4wd (has to be to have come with 275/70-18s) you have a massive selection of tires available to you. With such a large trailer and a single rear wheel truck, several of the tire options offer increased load carrying capacity too.
Toyo offers the Open Country A/T II All-Terrain in a 285/75-18 (35x11.50-18) Load E 129/126 sizing, it's load capacity is 3900lbs per tire in a single wheel application, up from 3640lb for the stock size tire and Mac 80psi cold pressure.
Nitto offers the Dura-Grappler which is more a highway rib tire in a 305/70-18 Load E 127/124 sizing with a 3750lbs per tire capacity and max 80psi.
The Toyo Open Country Mud Terrain that I run in 35x12.50-18 is Load E 123/121 with 3415lbs per tire capacity and max 65psi. They are just wide enough that the side lugs of the tread scuff the paint off the radius arms mounted on the stock wheels.
With the trailer you run, both of those LT Metric sizes are good choices, even though they are taller than stock by 2". Running the 285/75 or 305/70 at 65-70 psi front and 55-60 psi rear will net good wear and ride and the tire will not be under-inflated even when towing. I run 50psi front and 45psi rear, and ride quality is excellent on the larger floatation size. My 5er is only 30 feet, and max weight is 11,500lbs though, so I'm not quite as heavy as your rig. When I scaled my '05, the axle weights on a 20,000lb total combined were F:5,500 R:5,500 T: 9,000 and it towed great. The only thing I learned on my first big trip with that rig was to run lower pressure in the rear tires of the truck, I centered them out in about 9,000 miles of towing and still had 20,000 miles in the front tires.(I get 65-70k from the Toyo M/Ts).
Hope this helps.
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The Current Truck (Oct-2013 to Present):
1999 (Early) F-350 Lariat, CCLB, SRW, Black/Tan
7.3L Powerstroke, 4R100, 4x4, 3.73, 37x13.50-18s, '05 Axle Swap, 6" Fabtech lift, GTP38 "D66" turbo upgrade, SCT 4-position chip with custom tuning by me, Straight Piped 4" down pipe through 5" dual stacks, N-Fab full length triple steps, Pro-Tech cab guard and tool box, louvered 5th wheel gate, Hella 500 Fog and Driving lamps, much more to come...
The one I'll miss, (Mar-2009 to Jan-2014):
2000 Excursion XLT 4x4
6.8L V-10, 4R100, 4.30, 285/75-18, 271whp / 388wtq
The one I won't, (Jul-2005 to Sep-2012):
2005 F-350 XLT, CCLB, SRW, 4x4 FX4
6.0L PSD, ZF-6S650, 3.73, 35x12.5-18, 4.5" Lift