Got rear-ended at a stoplight 3 weeks ago and the other drivers insurance keeps stalling - what next?

Sitting at a red light three weeks ago, someone slammed into me going maybe 25mph. Their fault 100 percent, police report confirms it, they were cited. My car is drivable but the bumper, trunk, and rear quarter panel are all messed up. Body shop estimate came back at $7,800.

I filed with their insurance (a big national carrier, not naming names but you can probably guess) and at first they were responsive. Now its been 11 days since the adjuster last returned a call. I left three voicemails this week alone. They keep saying they need to "evaluate" the claim and "verify coverage" even though I sent the police report and photos within 48 hours.

My own insurance keeps telling me i can file under my collision coverage and let them subrogate, but i dont want my deductible tied up for months while they fight it out. Anyone been in this exact spot? Is it time to involve my state insurance commissioner or am i being impatient?