Setting aside the correctness in OP for the moment, what’s being said here is that you don’t actually need to break lightspeed. The foot would have to be moving asymptomaticly close to lightspeed, but not passing it. OP used an equasion that works classically, but we’re in territory where that model breaks down.

But if the math doesn’t work out that way, anyway, then whatever, classical equasions are fine.