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If it were mine I'd drain the oil and refill with good synthetic 5w-30 it's the best oil to ensure long life in all newer 6 and 8 cylinder Ford engines.
Yup, the Triton's were designed for 5w-30 and the only reason they changed the specification to 5w-20 was to get an extra .2 mpg sacrificing longevity in the process. The bottom ends are pretty much all the same and all changes to the later engines were minor mostly upgraded phasers, tensioners, and different flowing intake manifolds.
As the engine bearings wear and you start getting high miles it won't hurt to run a bit thicker oil but not necessary.
Thicker as in? 10w30? Or 5w30 - 5w40?
20W50 is for diesel engines