Well, went over the contacts with sandpaper, and put the starter motor in, and it started without hesitation first time and did everything a starter motor is supposed to do. Problem solved? Maybe. Have fingers crossed.
Took the back off the starter motor that was on the car, and WOW. The contacts are like a hundred times worse than the ones that I photographed before, one side is so worn that it's so thin that the edges just flake straight off...