It seems like you're trying to train yourself not to need the attachment so much. But maybe instead of trying to get rid of the natural need, you could work on finding ways to fulfill it. Both by asking your therapist for more nurture, and by developping more nurturing bonds in the rest of your life.

Maybe you would want more. But would that be a bad thing? What do you feel would happen?

I'm working on very similar issues at the moment, about attachment, letting people get close to me, and how to accept support and sympathy. It's so scary. I'm coming to see that a lot of the fear is rooted in the past, not the present, and very very gradually starting to change my behavior and assumptions.