If you get convicted, the consequences will be harsher than any other traffic violation. It is a major offence and insurance company will not take it lightly. You should absolutely request a trial for this charge. From there, you can either get a lawyer/paralegal right away and let them handle it, or wait for trial date, and try to negotiate a plea bargain with a prosecutor. If you pick the latter and are not happy with the plea bargain offer, I think you should be able to ask the court to reschedule the trial so you can get legal guidance.
I do think your chances of getting it reduced, if not thrown out entirely, are pretty good. I have seen people get "improper left turn" charges for causing real accidents with major injuries, a "near miss" like that should not get "careless driving".