Full synthetic in a regular V8 F150 is a waste of oil. Cobra, Raptor, OK. But there is nothing especially wrong with the standard 4.6 that expensive oil will fix. It's a budget, low output, workhorse engine. The flaws in the 4.6, like other engines, will show up regardless of oil type.
In other news. Engine was designed for 5w30. 5w20 is for emissions. The difference between them, in a healthy engine, is negligible. 15w40 in warm climates and industrial applications with a block heater. I've even seen 5w50 in built 4.6L's for racing. I run 5w30 in Ford Modulars, 10w30 for track days.
Just use quality oil. Motrocraft Half Synth, Castrol, Mobile1, etc. Amsoil, Total Quartz 9000, and Repsol, are way overkill. Check your PCV, and do your own changes. 3 qt's low ain't going to hurt a healthy 4.6L as long as it wasn't ticking. Keep the level in the middle. Some modulars will drink the oil if you fill it clear to the top of the stick. For example, my Mustang takes 6 qt's, I only put 5 in. I add a pint of STP first (old habits, but seems to work).