The current astroturf grips so much because tires hook into it and the rubber that may deposits in/on it - a material that doesn't allow that (as much) would fix the problem... At an indoor track here in the Netherlands they use porous plastic floor tiles for low-grip areas in the track, where funnily enough you get more traction as your tire wears down.
That, or change to a regulation tire that offers less bite and preferably even one that has long-lasting performance instead of a short spike in performance. If you can engineer tires to generate more grip, you can also reverse the process to reduce grip
