I'd like to give you a solution, but frankly 10 years after your conviction, you are well outside of the window of opportunity to appeal this or have a lawyer do a 440 motion. About the only legal grounds that you would have for reopening it would be if there was no newly discovered evidence of the sort that could not have been known at the time of your conviction and which, had it been known, would have caused the case to come out in your favor with an acquittal or dismissal. Your fact pattens indicate no such evidence.
So, you have no remedy uner NYS law. The judge can howver, grant you relief under principles of equity. That is, he has the power to dismiss a case if he feels it is the right thing to do in order to remedy an injustice done to the complainant. The motion, which is sophisticated and should be done by a lawyer, is called a Clayton motion and/or a motion for a matter to be dismissed in the interest of justice. You can see the authority for that in this section of the law here. (see CPL 210.40
It is a special remedy, because the state of New York has a vested interest in wanting its criminal convictions to stick. They are usually granted under highly compelling or extraordinary circumstances. But it's all you've got left, apart from the Certificate of Relie from Civil Disabilities or Certificate of Good Conduct which you say you don't want.
If you're interested, you should sit down with a local criminal lawyer and he can tell you whether he thinks it would fly so that you can determine for yourself whether the expense of the legal work will be worth the price. If you don't have a lawyer you want to use for this, you can find a criminal lawyer through the NYS Bar Association's Lawyer Referral Service.