I'm unconvinced that compensatory movements on pedals are a good idea or even help much. The main risk with toeclips or SPD-like pedals is having the angle wrong and stressing knees.
One easy way round that is to wear shoes loosely. SPD shoes are pretty rigid affairs, if you lace them up loosely your foot can swell, move about a bit; but no way are you going to pull your foot out of the shoe.
WCTD, as a member of the wobbly brigade, you have my sympathy. My vertigo (which was migraine related) was appalling when moving for some years. I couldn't walk without a stick. I hope the medics can find a solution for you.