You should invoke the appraisal clause in your policy. You hire an independent appraiser, he negotiates with the insurance company's independent appraiser, and them come up to an agreed value, which is binding. Takes the insurance adjuster out of the equation and their crappy valuation system.
Not to be creepy but I ran the vin from your plate and got a value around $35k off the bat based on comparables, book guide came in at $38k but that does not carry much weight. Could go higher, or lower, if I had more details.
What value are they giving you?
I can DM you a few appraisal companies that I've worked with before that are pretty fair.
$300-$500 on average. Some companies just sell reports for $300 which are useless. You're still playing on the the ins co's turf and have to dispute the report against an expert valuator brainwashed to defend low values.
OP's independent appraiser would work with the ins company's appraiser, that is, the ins co hires an independent appraiser as well, on their own dime. Their employee, and report, are no longer in the picture. If the 2 appraiser's methodology is solid and fair, then both of their numbers should be similar as well.
That's the important part here, the appraisal clause is a carve out where 2 appraisers duke it out, so no one is negotiating with the ins co, which is practicing law.
OP needs an NC licensed appraiser.