I agree with you size 13s are a little harder to find. When I was looking at new tires, I was considering up sizing to 14" rims too.
Here are a couple notes I took while researching tire options;
Per Jayco customer Service
Clearance between the tire and the wheel well or other interference needs to be a minimum of 2.5"
Recommend contacting Dexter (axle provider) to determine if they have a solution for larger tire sizes, such as a lift kit or something else. Dexter may also have a maximum tire size recommendation for our configuration
Dexter axle:
Torflex 2000
Part # 0263596
Frame Info;
Bal Industries
Dual axle JB Frame
Part # 0207660
Per Dexter Customer Service
Need to have a 3" minimum clearance above the tire to wheel well/interference, that is with a full load condition.
Need to have a minimum of 1.5" clearance between the wheels on a tandem axle unit.
I upgraded to Carlisle load D, don't recall which model. Discount Tire informed me of the tire, as they were very new to the market at that time. I have liked them so far.