I have an identical problem and very frustrating to hear the induction fan cycle on and off. I suspected the pressure switch to be the problem and took the rubber hose from the induction fan and blew into it and sucked out of it 10 to 15 times so it cycled the pressure switch. That seems to have solved my problem, at least temporarily. I also cleaned off the discoloration on the sensor as you did and I'll see if that helps.
This issue is very unfortunate, but somewhat relieved to know I don't have the only problem furnace.