I haven't read any of the posts, so forgive me if this has already been suggested, but...
...your horse needs to be taught to yield to pressure. Her basic instinct is to resist and pressure, and to fight restraint. Any attempt to tie her securely and allow her to fight till she succumbs amounts to abuse, particularly when there is a kinder, more sensible way to teach her to tie.
First, you need to use a pressure halter and, working the filly in-hand, put a bit of pressure on to ask her to simply move her head to one side. When she moves her head back to where it was, simply use a firm tug to bring it back to where you want it. As she yields to the tug, you need to immediately release the pressure. The tug is only a signal to the filly, and should not be a pull against her as that would nly cause resistance.
Two or three 'placings' of her head to one side should be quickly followed by the same to the other. Then teach her to step forward, using the same pressure and release Then ask her to step back, using light pressure on the halter and a hand against her chest. If she resists, just release the pressure and try again. She will quickly learn. Watch her body weight shift backward and release te pressure at that pint and the step back should follow.
It's about light application of pressure and timely release.
Once she has learned to yield to pressure, take a long rope from her halter and run it through a tie ring, and step away from the filly, holding the end of the rope and keeping a bit of tension on it. If she decides to pull back you can 'play' her on the rope, whilst staying out of the danger zone, and, by taking and giving the rope, encourage her to settle. When she stops going backwards it is a simple thing, because she has already been correctly taught to yield to pressure, to use a bit of pressure to ask her to step forward again.
If she takes a serious pull just don't pull against her. Without anything to resist she will be unlikely to pull hard or to rear. By giving the rope and releasing the pressure you will avoid her flight response, and she will settle and be ready to continue her training.
This is the method I use with all horses, from foals to unhandled three year olds to adult horses which have missed this vital part of their training. Within thirty minutes or so they have learned to tie without pulling.
It's about teaching them to accept being tied, not tying them before they are prepared and risking injury or permanent psychological damage.