I think this too mixes AP with LS when they are distinct things in this context. While TK can have AP when used to accelerate an object at high speeds, simply applying force to restrain or push someone does not inherently equate to an AP based attack. If something is being moved at a high speed, the damage comes from the kinetic energy, not from just being pushed. If Kat’s stasis field applies force to "paralyze" or push an opponent, it remains a matter of LS—only when she uses it to cause acceleration would it act as an AP based attack. Since the Headmaster has higher LS, he resists the force outright.
I think your Mach 500 analogy assumes that force applied by TK automatically translates into damage regardless of movement or impact...like before.
However, being hit with a force that could launch someone at Mach 500 is not the same as actually being launched at that speed. The damage in your example would result from the immense acceleration tearing the body apart, which would only be a thing if the object is moved at such speeds successfully. Since the LS advantage would prevent the motion from happening, then no acceleration or impact happens, meaning no AP. Here since the Headmaster is strong enough to resist with LS, the AP effect never happens at high speed, and the force remains an LS vs LS rather than an AP.
Also, I am still confused since before one of you mentioned that it (TK) simply spawns on the opponent, so like, it's inherently no AP here. Don't know why I'm having this long conversation about AP vs LS. Not to mention, nothing stops Headmaster from using
Magic based TK to counteract her. He won't do it immediately, since as I've said before his standard tactic is Hua Jin, but it's entirely possible if needed.