Can you share an item with her? Like a blanket or the scarf? She charges it up by holding it, and then you can use her energy she puts into the item? I assume something soft would be preferable as touch is soft.

Why are you not facing eachother? Simply because it's too much for you? That might be a good goal for you. L's eye contact is difficult at times, but seeing her facial expressions are comforting to me. Maybe if the furniture is not set up for face to face, you could sit on the floor?