Just grasping at straws here. I remember in the old days, American Fords were known to have weak ring gears, and could have a condition where the starter would lock. Owners facing this condition were careful to park where they could easily budge the car, moving the ring gear a smidge and allowing the starter to engage normally.
And did you say you swapped starters ? Just wondering about the solenoid repair kit that is available.
Either something is preventing the starter from turning, or, as it sounds, a click 90% of the time is not enough electrons are reaching the windings in the starter motor, because a battery (much discussion here in past years about the deceiving reading of a meter, and the need for.a load test to understand what the battery is really doing when called to serve) - or, there is a significant drain somewhere competing with the starter when the button is pushed, making the battery carry its load, uphill, as it were.