This is the CAT Scale with my Can-Am Spyder and Yamaha R1 in the back including 1 battery and 2 x 20lbs propane tanks full. The water tank is empty though.
From the CAT Scale printout:
Steer Axle @ 2580 lbs. That is 175lbs under max for the Taco (2755)
Rear Axle @ 2840 lbs. That is 270 lbs under max (3110)
Total truck is at 5,420 lbs, or a scant 30 lbs under GVWR (5,450)
In other words, this is right at the maximum rating for the truck, but not over.
Assuming that scale weight was with you and your wife in the truck. If not, then your truck will be over GVWR by adding just passengers and drivers, much less any other gear you'd bring with you camping.....
Trailer axle @ 5100 puts the GCVW at 10,520 lbs, or 660 lbs under the GCWR of the Taco (11,180 lbs, 4x4 Quad GRN245L-PRADKA). Again, that is assuming the total scale weight includes passengers and driver. If not, then you'd be over the weight rating of the Taco.
On your F150, same thing applies, don't worry about the "payload" but what the "Steer", "Drive" and "Trailer" axle weights come in at. Looking at the F150 manual, you should have 17,100 lbs of GCWR, which is 6,000 lbs more than the Taco. I'm actually surprised that GCWR is that high from a 3.5L Ecoboost setup, but that is what it says. The 6.2L has the same GCWR.