Your best bet is to probably replace your wheels with something like a 16" or 17" rim. This will open up your choices for a true LT tire. Likely a D rating is plenty for your truck. Over the years you will buy several sets of tires and it will be easier every time to find the right size. Also, if you're in the middle of nowhere and put a large hole in one somehow it will be easier to find a replacement.
I would tow with P rated tires. They will squirm around under the load. They're designed to ride soft, not hold up weight.