To me, your idea ('come March' < 'if March come') is fluid and the connection works without 'when' and, moreover, without having to explain 'if', as there is no reason to assume that the adverbial phrase 'come March' somehow incorporates the meaning expressed by 'if'. It doesn't; e.g., in 'come March the roads will open', the reality is that the roads may or may not open, but come hell or high water, March will arrive. There is no condition there, no 'if' meaning housed in 'come March'. That is, March will arrive whether the roads open or not.
As I said earlier, I like your analysis.