I wouldn't try to change anything yet. Give it another month and see how your next period goes. You are right about how losing fat messes with your hormones, but the effect does seem to taper off over time from what I've read. It happened to me back when I was on a very low-carb diet, the first period was **** - but the one after that was pretty much normal. I'm pretty sure that further making your hormones wonky by going off your birth control will not make things better in the short-term anyway.
29 / f / 5'7"