Matt,

If wearing your ring is what you want, then do it. It is for YOU. You cannot do things to get a reaction from W. Doesn't work at all.

As for giving W back rubs, I am thinking that one's a no-go. She isn't interested in them at all as evidenced by her pulling back and other actions.

From now and on, you'll have to view and treat W as a housemate who comes and goes. You will do the same too. Take care of yourself.