Arbitrariness of the sign is a principle that requires so many epicycles to present as "true" that it's more of a warning against overgeneralization than an insight with any significant predictive power in its own right.
Let's call the arbitrariness of the sign, blinga. Why do you think blinga requires "epicycles"? Blinga makes pretty modest claims: there is no requirement that the form of a sign matches that which it signifies in any way.