It's possible you might have gotten more views in the F150 section, but I think it belongs here, and, once you create a thread (or a post), you don't have the power to delete it! (I expect that's because it can have a bearing on other posts in the thread.)
Anyway, glad you posted a picture. I suspect your trailer is 8 feet wide (standard width). Looking at the picture, it might be 7 feet high? (Box height, and 1 foot off the road?).
Now, with a class IV trailer tow package, the frontal area limit is 60 square feet. If your trailer is 8 x 7, you are at 56 square feet and very close to the limit.
Your tires have a 33" diameter (unloaded). If I were to mount your rims and tires on my truck with its 3.73 gearing and 32" tires, it would reduce my effective gearing to 3.62. I don't know what your stock tires were, but it's clear that your effective gearing is now much less than 3.55.
I'm guessing the empty weight of your trailer is 3-4000#?
In any case, I think you are very close to the tow limit of your truck. If you can afford it, changing your axle gearing to 4.10 would make towing a lot more enjoyable. (Both axles if you have 4WD).
Now, why were the RPMs in 3rd gear with O/D off higher than they were in 3rd with the O/D on? Probably, as Westcoast mentioned, your Torque Converter was unlocked in the higher RPM case. It would take very little additional load on the engine to cause the TC to unlock, which it does to provide you more torque. I think that at the speed you were traveling, your engine load is right at the "breakpoint". Again, higher gearing will help this situation.
And, if you want to talk to someone at PHP, try their "live chat" feature you can sign up for on their webpage. Their phones are ALWAYS busy and they really don't take phone "messages". But, if you keep trying, you'll eventually get through (you may become an old man first though).
- Jack