To me, if the point is you want horse to stand still? Making horse move makes no sense.
Teach horse a "be still" command verbally, and by correcting horse for moving period, on ties, while grooming. Can use whatever works for you, I also have used "keep those feet still" and "plant 'em".
And make sure offside rein is slightly tighter, so that if horse moves, it is coming under you too.
Bring horse up to block, tell them to be still, tighten off rein and then get in saddle. Make sure there is no poking, you are not hanging off of saddle too long and not plopping down in saddle or dragging foot across.
And then when you are mounted, stand still.
Also need to work on horse standing still when leading by you stopping and just staying still.
But your mechanics have more than likely caused this. Also would wonder if there are other areas horse is doing what it wants, but it isn't a problem yet?
Horses make me a better person.