Where did you get those payloads from? The range of payload for all 3 brands of 3/4 ton crew cab pickups is under 2000 to over 3000 pounds.
Check the dimensions of every crew cab 6.5' bed pickup,half ton and 1-ton are all very close in every dimension. I don't understand how the heavy duty trucks are considered big. Their styling may make them appear big, but they are all very close in dimensions.
In order to get 2400 pounds of payload in an F-150 crew cab, you'll probably have to customer order it with the HD payload package. They are very rare to find on dealer lots.
Consider tongue weight limitations as well. The 3/4 tons are 1400+ pounds where the F-150 is 1000-1250.