A 600$ late fee?
How exactly did they reject your attempts to pay?
I would be straight up with them and tell them I am not paying a cent more. I would let them know that if the matter needs to go to court that’s fine with me. I would thoroughly document (dates/times/details/names) the process so far because even though they don’t have jurisdiction over you in the first place, it sounds like they have broken their own “debt” recovery protocol by a) rejecting your attempts to pay and b) not allowing an extension prior to taking legal action. Certainly if you have been in contact with them through this process and not just had your head in the sand, you may be able to beat them at their own game on such a technicality as not following due process. I will look back through my emails with them to see their “debt” recovery process and get back to you.
Have you read the Know Your Rights book? The Fines section is pretty straightforward. For them to claim that you owe them money they must be able to prove it. And they simply can’t do that.