I had the same challenge with my TB X WB mare and also attempted to correct her walking off by backing her. Unfortunately, it only led to her immediately backing up as soon as I stood on the mounting block, so I had to get a little creative. We have a round pen set up at one end of the arena, which has proven to be quite handy for many things.
I started lining up Tessa in the corner, with her rear end and one side against the wall and the round pen in front of her. The only easy way for her to move was towards me. We did this just a couple days, and then I removed one "block" at a time until she would stand quietly wherever we were. Occasionally she'll still try to walk off too soon, and I go right back to the kitty corner spot, and mount, dismount, mount, dismount until I feel good about it again.
I should also note that this mare is 12 y.o. And really sensible despite all the holes in her training.