Reply by Loren

Poly takes awhile to firm up enough to take steel wool.

I rarely use real steel wool anymore, because the fibers come off
and cause problems like you experienced. The synthetic steel wool
is much better – more like a scrubbing pad.

Between coats I usually use stearated sandpaper. 150 or 180 grit
works well for most finishing jobs. You can remove the stearate
left behind by brushing or blowing with air, then a tack cloth. You
can also just brush the stearate off and re-coat. In my experience
the white stearate dust seems to dissolve into the next coat.