What happens next in car accident dispute/settlement?

The insurance company works for the other driver.  If the other driver says you were at fault, then their insurance company basically says, "If you say so, then we will not cover the claim."  Now, the reason the other driver does this is because the other driver doesn't want their rates to go up, but when the other driver does this, by freeing the insurance company of liability, they take on the liability themselves.  So filing suit against the other driver in small claims court was the smart thing to do.

You don't need to worry about lawyers because lawyers aren't just not required for small claims court, but also they're not even allowed.  You don't need to worry about the insurance company's lawyers giving you the run around, either, because they washed their hands of it entirely as soon as the insured, their customer, said it wasn't their fault.  That frees them from anything and everything.  So it's just you against the other driver in small claims court.

So when you show up for small claims court, be sure to have the evidence  you say you have ready to show the judge.  Like you say, it'll be a slam dunk.  When the case is awarded against the other driver, the driver will be obliged to pay you, and what will in all likelihood happen is the other driver will go back to their insurance company and revise their statement, and with a finding of fact by the court, the insurance company won't be able to quibble but will just have to pay the claim in accordance with the judgment, but if the driver doesn't do that, then the driver will have to pay the money to the court, which will in turn pay you.

Unfortunately, without insurance, you will need an attorney to fight this in court. Don't expect any attorney to take this on a contingency because winning the case is reasonably doubtful.

Your video means nothing. Nor does the police video. Just because he said he was at fault doesn't mean he actually was.

you werent legal to be on the road yet you were. You are at fault. Your car should have been parked and your butt in an uber or bus. You may not have caused the wreck but you were driving illegally. You cannot win a case sorry

Consult a lawyer who can review your case and advise you of the best course of action.

You'll get the run-around everywhere, including the police. You need lawyer. The next question then is would it be worth it?

You just need to hire an accident attorney.  If your case is really that strong they will work for "free" and get the insurance to pay his fees.  

Regardless most people would just claim on their own insurance as no fault and your insurance company will have lawyers go after the other driver and refund your deductible and any other expenses you may have paid.  There's no reason to have to go in on your own in small claims court.