Washer has a loud, deep, rhythmic rattle which sounds like it comes from the center, maybe near the bottom of the agitator. The wash loads are always carefully balanced and the washer is level.

Does noise only occur during spin cycle?

Yes, both after the wash and after the rinse.

Is the drain hose sealed to the washer stand pipe or is it just hanging in the pipe?

The drain hose is just hanging in the pipe.

Turned out I had to replace the idler wheel pulley. The drive belt goes around it. The plastic wheel was laying on the floor of the washer and its metal liner was still on the shaft. I had to remove the retaining ring at the bottom of the shaft so the liner would come off (with assorted washers), and then replace it with a new one. It wasn't as easy as it sounds because access was almost impossible. Now the washer is nice and quiet. Maybe this answer will help someone else.