Thanks astraelraen. I think I get it now, and I also think that the builder website gives the wrong max payload for the Lariat. I see now with the right configuration (SCrew, 6-1/2 foot bed, and 3.73 Limited Slip, the HD Payload Package appears on the next screen. The only thing is the website shows the non-HD Payload Package payload. Looking at the 2013 Source Book
I think the payload should be around 2,310 lbs (minus options). The best part of the HS Payload Package is that nearly all the extra payload capacity is on the rear axle.
BTW - The reason I mentioned towing but talk about payload is because hitch weight is a percentage of trailer weight, 10% to 15%. A good way to calculate how much can be towed is to subtract people/dogs/and junk in bed weight from payload. Take the remainder and divide by 0.15. That will give a good approximation of maximum trailer weight for your truck. That mythical 11,300 lb trailer is unlikely to ever see a F-150 because its hitch weight alone would probably exceed the rated hitch capacity of the truck.
It's too bad Ford doesn't just include the HD Payload Package to all models. It only adds 60 lbs but does so much to make the truck more useful.