First and foremost, we buy what we can afford and no one can argue with our personal budgets. If you don't have the $$ than the P-Rated Wranglers will have to do the job.
Second, I trust the judgement of the folks at River Runners because they run that shuttle everyday with multiple rigs; the key is they are recommending the most appropriate tire for that road but not necessarily what is best for your truck year round. We transitioned to LT rated tires last summer because of Deso and I haul firewood off dirt roads on USFS and BLM lands. We went with the LT-rated Wrangler A/T w. Kevlar. Several of our friends have experienced flats on that road whicg can jeopardize a trip fast.
People are correct that the load range goes up with LT-rated tires. That is a benefit of their beefier construction, especially in the sidewalls. When you compare most LT tired to their P-rated breatheren you will see thy tend to have more plies. Not only that but that are made with higher quality steel belting for the plies. The tread is also better designed for off-road use, mud and snow than P-Rated tires. The principle change in use for owners will be the fact that LT-rated need to be inflated to higher pressures to carry the same load; my tires sit at 45 PSI for average loads but are designed to be inflated to 80 PSI. Most P-rated tires max out at 35 PSI.
Make no mistake, an ideal tire for dirt roads and loads would be an LT-rated tire. Manufacturers put P-rated tires on trucks and SUVs because 1) most people only drive paved roads with them, 2) they are quieter and get better MPG and 3) they are cheaper to produce which is key to price pointing cars off the lot. Those are all realities of their tread design (efficiency over traction) and weight (fewer plies).
If you are not on dirt much the decision is much harder. Its expensive to put a LT-rated tire on a truck/SUV that only sees dirt once a year. On the other hand, if you primarily run rivers in Utah (Sandwash Rd, Clay Hills shuttle, etc), camp in southern Utah in places like the Escalante, and carry any loads (most curb weight trucks are already at 60-70% load capacity of P-rated tires) than justifying LT-rated tires becomes easier.
If you stick to P-rate tires just 1) keep loads lighter, 2) drive slow down the Deso road, 3) be very aware of road conditions for your sidewalls and 4) have a full-size spare and checks its pressure before you leave.
Have a great trip. Missing our normal summer Deso trip.