A tad outside your price range, but the original Mostile 1963 driving shoes are still made, albeit by part of the Prada conglomerate, which is generally disliked on this forum.
I confess I have never quite got the point of them. They seem to be "an answer to a question that no-one asked" ((c) the late Col Jeff Cooper).
I presume Sebastian Vettel wears some kind of Nomex ankle boot. I cannot recall my own shoes ever slipping off the pedals of a variety of cars. And there is something risible about a man wearing Italian suede driving shoes and getting into a Civic, Prius or Camry. Or riding the subway.
If someone can tell me that Stirling Moss or the late Jim Clark liked them, I shall consider revising my prejudices.