How can you sue your insurance company for a first party claim?
As an insurance lawyer I can tell you that in the vast majority of States, yes you can sue your insurer despite any mandatory arb provision. To hold otherwise would be circumvent each State's law as to insurer bad faith.
What often happens-not saying it happened here-is that the insured submits an inflated claim, substituting current versions of a product for a product no longer in production, getting estimates from a vendor in a wink-wink scenario in which the vendor wants the sale(s), ignoring depreciation and fair market value, to name a few.
Claim reps don't know about audio so they do what anyone would do-they ask questions and do a little research.
I am not here to dispense advice but talking to your agent, reading your policy, taking photos of your gear in your home and keeping receipts and records are all good things to do.