Morally, you're correct. Realistically, you're going to get reamed.
If you ask them why it took them so long to catch up with you, after you've already said that you accelerated past the lights, that's not going to end well. They don't have to do you for speeding as well, just the red light jumping as it's a more serious offence.
It's up to you, of course, but I hope you've got deep pockets for a good solicitor. Do NOT try and do this on your own. *EDIT* Ah, you said you're going to get that sorted. Good luck.