Who's towing with a F-150 5.0 Liter

Hi there, I have a 2013 F-150 5.0 3.55 FX4. 7350 GVWR 1340 Lbs payload. Currently towing a Jayco 228 ultra lite, 4875 Lbs loaded including water. We drove from Edmonton Alberta through the Canadian Rockies including going both directions on the Cocquihalla highway in British Columbia (8% grade on one stretch for several kilometers). Total mileage for that trip was just over 3300 kilometers. We have myself, The wife and our three kids. With our bikes in the box we were 300 Lbs over the GVWR and 900 Lbs short of the GCWR. For the trip the truck towed the trailer effortlessly. Other that a couple of stretches on the higher grades the truck drove in 5th gear at 2100 RPM. On higher grades the truck would drop to 4th and sometimes into 3rd but they were short stretches and maybe for around 20 minutes. We did have one stretch where we left Kamloops BC, the outside temp was 39 degrees Celcius and the transmission was getting hot so I had to drop down to 80 Kms for a bit to allow it to cool (it was about 6% grade for that stretch of highway). Once it cooled off I ramped it back up to 100 Kms and continued on. For our size of trailer the 5.0 is an excellent motor. We are looking at upgrading the trailer in the next bit to something longer and with a slide. I am estimating the trailer to be around 7500 Lbs once loaded with gear and water. I am very apprehensive about being able to tow with the 5.0. First due to it overloading the truck and second due to lack of power to tow that large of trailer. We will have to replace the truck to upgrade the trailer but I will not be getting another 5.0 with better payload. I am either going to mover over to the Ecoboost with the max tow package or we will upgrade to an F-250 with a 6.2 (do not need nor want a diesel). From what I have heard from others who own a F-150 5.0 and have read, this motor is excellent for towing but the limit is around 6500 Lbs. Anything over and you will want to look at something bigger. As well for a daily driver I really enjoy the truck. It averages 16 mpg and has plenty of power when unloaded. That's my two cents. Ryan