Interesting info from equill and Unknown_K. I'm pretty much certain these are 1.44 MB drives, and the cable I was using most recently has a red stripe. I didn't know about the stripes, though - that's very interesting.

The methods described of cleaning and greasing are exactly what I have done, even the part about WD-40 to clear the old grease, then applying new grease. White lithium grease is what I used which I believe is the original kind used.

I have a feeling that it's a problem with the heads, and possibly a problem with how much pressure the heads are having against the disk surface. On one drive, I wasn't completely convinced it was even touching. That particular one may have been a cheaper manual-inject drive come to think of it.