Hi Andy,
Good post - a topic I think about constantly, and I am slightly embarrassed to be contributing now: I have a penchant for buying ever new and "better" watch boxes- not just for storage, but for "displaying" so I can marvel over them and/or convenient storage so I can put directly/easily into my winding cabinet if I choose to.
My favorite watch display/storage box (which is actually a discontinued form of remote control box), chiefly because I get to see them dial up smiling at me :) Drawback: if you put them onto a winder cushion, they can't fit into this particular one.

More 'updated' remote control type boxes, which are larger - though a bit too high for me to see the watches



A neat recent acquisition, that slots like in a winder. Drawback: can't put too many watches:

More conventional storage box

too many !

As to whether keeping them wrapped around a cushion is healthy - my opinion is: its ok, but not a great situation if its done too long, so getting them out for wrist time is important to me.