I wouldn’t use anything oily inside the cooling system, as it will coat the entire system possibly causing a loss of heat transfer.
Also, I have used muriatic acid on things before but it’s very dangerous and the fumes can kill you.
I would only use it if I could stay completely away from it while it cooked.
White vinegar is fine, just takes longer, but safe.
I would give a block a couple of days soak, then rinse with water.