Definitely probably do not call them and tell them that now that you have been in an accident with a state vehicle, and fault is in question, you'd like to get your lapsed insurance squared up

They're going to express how absolutely fucking elated that they are to hear that your insurance lapsed before you got assblasted by a plow truck, and that's about it

You might (NotLegalOrIllegalAdvice) have better luck, if you're not too far outside of coverage, calling and trying to get your shit reinstated without mentioning the accident

Considering that as soon as you submit that claim, they're going to fucking eagle-eye your entire shit, and that you are going to be getting into it with the State, I'm not entirely sure how deep you want to get into trying to submit a claim under lapsed insurance in that circumstance

This, 100%

Sorry to tell you, but the likelihood is very high that you fucked yourself by trying to be a good guy and answer her questions

I made this same mistake myself once

I was struck by another driver making a turn and coming out of their lane and hitting my car in the parking lane on the side of the road - Cops showed up, police report was written up as them being at fault, with a whole fucking drawn up visual of the accident, their car coming out of the lane and striking mine, shit was circled, the whole ordeal

A day or two later, I get a call from an insurance agent - their insurance agent - claiming he wanted to go over the accident and get an idea of what happened, the whole good guy bit

I answered the questions and explained the situation honestly

They proceeded to somehow get an amended police report that stated they were actually not at fault - My insurance company said they had never seen it happen before

She was absolutely not calling you to be your friend and chat - Her job is to, in a very strategic, calculated and predatory manner, determine your level of legal capability, the level of their own exposure, and how likely it is they are going to being held liable and made to pay out

By telling her that where you were parked was, even potentially, stupid on your part you admitted that your own actions put your car at risk, and by telling her that you have no insurance or concrete evidence of them being at fault, you exposed that your means of recourse are pretty limited

Unfortunately, they're probably chalking this one up as pretty low priority - In my relatively meaningless opinion, pursuing a lawyer is probably the right move