Well, since the tow capacity of my 4x4 V10 with the 3.73 rear end tops out at 9000#, give or take, coupled with the fact my TT dry at is 4500#, and no more than 7000# loaded, I can't say how a topped out Ex at 11K would handle. BUT, we've taken her to Yellowstone 4x from VA and always made it back no issues. The key with the V10 is to keep it tached up at 3000 to 4000 RPM on grades.
The weak links with pulling 11K (which by the way is the max tow capacity for both the 7.3 and V10) is the suspension and the gutless 4R100 tranny. Plenty has been written on fixes at the Ford Truck Enthusiasts website forum.
Good luck.