It's more like 15 degrees some say ford says 20.
Actually sounds pretty good for what you thought you would have at first. . They are loud engines. I would remove the cat and leave the muffler. The cat is useless and restricts exhaust flow. I doubt you want a straight piped 6.0 though. The muffler doesn't restrict that much.
I know this sounds dumb but I would get a flash tuner and through a nice heavy tow tune on it. Should wake the engine up a bit but they are super safe and will actually make it a better truck.
The 5r110 is a good trans but they do go out. Maybe do a fluid flush?
Any residue around the coolant res? Coolant flush is needed if it doesn't have Low silica coolant. That is what clogs the oil cooler and egr.
Your egr has a valve on the intake horn. That sucks but oh well. You might want to pull the EGR valve out and clean it. A good tuner can turn it off and save you that hassle. On a good note, the egr coolers for 03/04 are the stronger design.
Try some rev-x in the engine. Will cost you 70$ but it does help the injectors and should smooth out the idle.
A cheaper version is evergreens archoil 9100. Works for some better than rev-x and listening to your idle, I think it might give you better results than I got. I have a bad injector though.