My view is that you won't be able to remove the need for CA on super-high-grip carpet without changing the construction of the tyres.
Compared to a full-size rubber tyre, and RC tyre is only supported by the insert (which has a large unpressurised airgap between it and the tyre, and the belt is very simple. There is no particular structure to the sidewalls (maybe the rubber is a bit thicker).
As soon as you start cornering, the tyre sidewall collapses inwards - generating a bunch of unwanted grip. I wouldn't be surprised if the collapsed sidewall actually creates a bit of a peak in the contact patch initially as well, which probably makes the grabbing worse.
CA is a very effective way of taking that part of the sidewall out of the grip equation and at taking the "edginess" out of a car.
We end up glueing the sidewalls of Mini tyres all the time on carpet, and if I race my TT-01 on carpet glueing is the best way of stopping it from rolling all the time.
I think some of the Japanese tyre manufacturers have done "special front" tyres in the past for Mins, but I have never tried them.
If you built a true radial RC tyre you might get some different results.