Lots more about this subject in
this BIA document. In particular, very near to the bottom of that document it mentions the 2 year clear period as regards fines, already mentioned above.
lancoalase, I think you have a problem. I think you should draw BIA's attention to the fine as soon as possible, and at the very least, don't be surprised if they sit on the application at least until August, 2 years after your date of conviction.
And it might be worse, they could simply reject the application, and whilst it would not stop you applying again, after the 2nd anniversary of your conviction in August, it will of course add to the expense of becoming Naturalised.