Insurer offered $8,500 for my totaled car. KBB says $14,200. How do I fight this?

My 2021 Civic was rear-ended hard enough that the repair estimate came back at $12,000, which exceeded the car's value so they declared it a total loss. Fine, I understood that part. What I wasn't prepared for was the actual settlement offer. They came back with $8,500. I looked it up on KBB before I called them back and the private party value for my car with its mileage and options is $13,400. Dealer retail is $15,900. I have no idea how they got to $8,500.

When I asked for their valuation report, the adjuster sent over a CCC One report. I'd never seen one of these before. It listed three "comparable vehicles" they used to calculate the value. Two of them were base trim LX models - my car is the Sport trim with Honda Sensing, heated seats, and a moonroof. The third comp was from a dealer 180 miles away. None of them were actually comparable to my car. They'd also applied something called a "typical negotiation adjustment" that knocked off $600 from each comp, which apparently they're allowed to do but feels like they're just making up a discount.

I've read that you can dispute a total loss valuation but I don't really know how to do it effectively. Should I get an independent appraisal? Find my own comps and submit them? Is this the kind of thing worth calling a lawyer over, or is the gap small enough that I should just negotiate myself? Feeling pretty frustrated because I need a car and this is holding everything up.