Paying the ticket for failure to avoid an accident removes all presumption of innocence on that one. You are serving the agreed sentence so there is nothing you can do to get that "taken away". If you have a valid defense to the speeding citation, you may raise it at the court scheduled hearing.
If you have had no other tickets in the twelve months leading up to the speeding ticket (other than the accident ticket) you are still eligible to get court supervision on the speeding ticket. You cannot mail in for it, you must go to court to get supervision a second time in any twelve month period.
It would likely go smoother if you retained counsel to appear in court with you.
You are eligible for one more supervision if the one for the accident was the only one you received in the prior year. Be aware that receiving an additional supervision could violate the one you received for the accident.