Intrinsic spin in a rotating frame of reference? Thought experiment get me confused, how to deal with this paradox?

Consider a ring of stationary electrons fixed in a circle on the x-y plane around the z-axis, and an electron above the circle on the z-axis. That lone electron can have spin pointing either up or down the z-axis. Now by Coulomb force the lone electrons will be pushed up the z-axis.

But now consider a rotating frame of reference where the z-axis is fixed but the new x-y plane is rotating at some velocity w around the origin. In this frame of reference, the electrons are moving around the circle with velocity w, so it creates a magnetic field. This act on the lone electron because of its magnetic moment. The total force caused by this is dependent on total current, and hence w, and the spin of the electron. However, since intrinsic spin is quantized, it cannot be different between different reference frame, so it’s independent of w, and it can only take on 2 values for 2 directions, depends on which spin we chose in the beginning.

But because different frame of reference must predict the same final result, the electrons must still be moving up with the same acceleration. That means Coulomb force in this frame of reference must be altered to match. But because the magnetic force depends on the direction of intrinsic spin, Coulomb force must be dependent on intrinsic spin as well. But this sounds very wrong.

So is this conclusion correct? Intrinsic spin are independent on all frame of reference, and Coulomb force is dependent on intrinsic spin. Or am I wrong somewhere.