Okay, OP you've got some great advice going on here....I agree on all counts. Lose the saddle, it's way too wide...and if she pulls down push forward.
The only thing I have to add is that if she keeps backing up on you when you ask for forward(and I mean with a saddle that doesn't hurt), back her up til she won't anymore. Make it so that she WANTS to go forward. When she starts backing up and you don't want her to, continue to back her more, more, more, more, when she makes a move to go forward, relax and allow her to move freely. If she doesn't try to go forward, stop backing every now and then to offer that chance. If she doesn't accept, continue to back. I think you'll find that if she knows she has to work in one direction or the other, she'll choose forward :)