A couple additional thoughts:
Double check ALL battery cables, both red & black for good connections, ground cable to block typically gets forgotten about
OEM wiring on the Ford does have a remote relay/solenoid & if equipped is the likely culprit
Replacement permanent magnet starters for Ford & GM have the relay/solenoid mounted on the starter, and the OEM relay should be by-passed to eliminate double troubles. The new style starters have notoriously poor solenoid contacts inside.