Best thing to do is hire an attorney. Sounds like there may be some good defenses to this case. Also, an attorney should be able to negotiate a favorable resolution, which doesn't result in a conviction.
Yes, you should request a court date and not pay the ticket. You may have a chance at meeting your goal without an attorney. You can always schedule an appointment with a hearing officer and hopefully get a continuance for dismissal. If they don't offer that then you can set it for court and retain an attorney.
This send like a very defendable case. The time frame if not an absolute defense, but is very favorable for you. There doesn't seem to be a lot of evidence against you. You should contact an attorney and start fighting this case right away.
You will have to go through a hearing officer and possibly court in order to keep it off your record. It certainly is possible, but do not simply pay the ticket (that would result in a guilty plea and a conviction). The best way to have this is to avoid any type if conviction up front. It would be in your best interest to retain an attorney to represent you through this process. I wish you the best of luck.
A crash case could potentially be handled differently by the prosecutor and judge. There may be several legal issues that it would be wise to have looked at prior to entering any plea. It's important to consult with an experienced attorney who will represent your rights in court and make sure you ate making the most informed decision.
I hope you find this information helpful and I wish you the best of luck.