My insurance adjuster tried shorting me out of $1700 in value of my vehicle. I sent the guy three other vehicles of the same make and model and within 2-3,000 miles difference. I had to call his boss show what I had found and wanted a fair settlement.And it worked? You just made up some legal letterhead as a Letter of Representation?
Insurance is supposed to cover you everywhere. Sometimes the police won't come out if it's in a parking lot or someone's driveway unless the damage is extensive.
Progressive will subrogate for your deductible, let them deal with the hassle. It might take a few months. I doubt your rates will go up unless you have multiple accidents but it's very hard to answer this question.