My 2010 Fuzion triple axle toyhauler's GVWR is 18,000 lbs. and I have the Sailun G rated tires on it, which replace the horrible OEM tires. I've considered going to an E-rated LT tire, but I can buy G-rated Sailun tires for less than the LT tires.
I've weighed each wheel separately and have a max of 2700 lbs. on two tires, and the other 4 are 2500 lbs. or less. I run the G-rated Sailun tires at 90 psi, which gives me 3300 lbs./tire carrying capacity.
Why do you think the F-rated tire sidewalls will be stiffer than the E-rated? And if they were, that could easily result in a very rough ride. My thought would be if it ain't broke, don't fix it. :) That's assuming, of course, you can find a good E-rated ST tire.