You didn't indicate a year. But based on
Ford F-Series (Wikipedia)
it's good guess that you've got a
Ford C6 transmission - (Wikipedia)
I'd verify that, then discuss it with a good transmission mechanic to see if what you've got is shifting like it should. Kind of suspect it is, but I'm no expert. While you're talking it over with the mechanic, you might want to ask questions about conversion to a automatic/manual shift, valve body or a full manual shift, valve body. (As in would it be a plausible DIY project? - I don't believe
the parts are all that expensive compared to the probable gains FE.)
Something came up. Gotta go now. May post more on this later.