lock,
Solenoids can be problematic. There wouldn't be a chance that the ballast resistor was installed in the key switch line to the starter would their. This would not be right.
If the solenoid clicks, that means it is being pulled in by the key, it just isn't closing the contacts to spin the starter. This truck, unless a automatic, usually doesn't come with a key type starter. I don't know if this is possible, but if the starter drive gear was prevented from moving its full travel, maybe it is restricting the movement of the solenoid plunger which would tend to hold the internal switch open and possibly cause these problems.
As you mentioned, a funky key switch could be a problem, but if you hear the click of the solenoid, that means it is trying to pull in.
The solenoid circuit, after a momentary inrush, doesn't consume much current.
I would make sure all my battery cables were of ample size and in good condition, with good connections.
If you can upgrade to a better quality switch, and have the fellow working on the starter dissect the solenoid for a post mortem, it might give you some clues as to the cause of the problem.
Stuart