I never had the specific problem but feel that the "clutch dog" is binding or is damaged. My recollection of the shift cam is that the grooves are kinda sloppy looking. Surely if the shifting cam and the engagement pin inside the prop shaft, don't set the clutch dog to the right position, shifting could be irregular. Additionally for an engine of that vintage, the spring behind the pin (inside the prop shaft) may be weak.
Not sure as to your definition of "grinding noise" but rpm needs to be high enough for the engine to continue to run when at idle and shifter is engaged yet be slow enough for engagement to occur without "grinding". On my later model engines the manual calls for 675 +/- 50 rpms with the boat in the water, free to move, in F gear. I had an '88 115 Tower but forget the exact number for that engine. And as others have stated, snappy operation of the shifter...by you is the requirement.
The fact that you only had fuzz-metallic paste on your drain plug magnet is encouraging. You'll have that.....the reason Merc. put it there in the first place.