Have you tried walking with a pole? (Cudzo, Jurek pipe down) Either on hills with a walking version or in ski resorts with your ski pole? Having three points of contact, two always on the ground makes a fundamental difference to your stability. So much so, that many prefer two poles, especially walking and hill walking. For me, that's too much faff, but with a single pole you quickly adjust to using it as and when really needed and relegating to helping the rest of the time.
Been skiing now at least once a year, often more, for around thirty years and encountered all manner of resort conditions, and have a selection of shoe spikes/grip additions I've tried mostly for out of resort mountain walking. In resort, just normal walking boots (rather than shoes, the ankle support helps stability) and a pole.