I agree with Margo. I actually think all the stuff about 45 days and whether or not they processed your resignation and so on is irrelevant. At that stage you would have been entitled to be annoyed about it, and frankly if you had left on day 45, even if they weren't ready, you would have been fine. In my opinion, your notice period starts from when your resignation is submitted and received. If you gave it in on the 31st, it's not your problem if nobody did anything about it for 3 weeks. They can't refuse to start counting on the basis of 'lalalala I'm not reading my mail!'
However, once negotiations were opened, that becomes irrelevant. You agreed to stay until the end of February. If I were your employer, I would have treated that as a new contract, de facto if not de jure, and I would have expected you to honour it, and been put out that you didn't. It doesn't matter that February was your chosen date and not theirs. You committed to the end of February and possibly they had plans to use you - to get their money's worth, if you like - all the way to the end of the month.
I understand why you didn't stay - I think we all do - and I can see somebody in this position asking to be released from the last week or two weeks of work. From an employer's point of view, though? I would let somebody go, for goodwill, if it wasn't going to inconvenience me, and in point of fact, I can't stop you going. I can't force you to come in. But if I said no, I needed you to work to the end of the period you yourself had negotiated, and I had planned on, and you insisted on leaving, I wouldn't be impressed and if I was asked for a reference later, the word 'reliability' wouldn't appear in it.