We towed with an '03 2WD Expe with the 5.4 and I don't recall which rear end we had but suspect it was the 3.31. We never towed in any "real" mountains but I could tell that the Expe would have been "huffing" on the uphills. On the flat it's towing ability was "adequate".
Our "max tow" number was 8950# and our HTT weighed in at 4420# and we had 540# on the tongue (with the WDH) which left us 328# shy of the Rear GAWR. With just the Bride and I and a bit of gear the rear axle weighed 3100#.
My point is I think you will be close to the Rear GAWR even though you are well below the max tow #. You can see my weight #'s below.
2013 F-350 CC SB 2WD 6.7PS
2013 Eagle Premier 351 RLTS
-SOLD- 2012 X23B
-SOLD- 2003 Ford Expedition 5.4, Bilstein shocks