Hail damaged my roof in March. Insurance adjuster says 'minimal damage, patch repair.' My roofer says full replacement. What do I do?

We had a significant hailstorm in March. My neighbor's insurance paid for a full roof replacement. Several other houses on my street have had full replacements done since then. Mine is an 11-year-old shingle roof with no prior damage that I'm aware of.

My insurance adjuster came out about three weeks after the storm. He was up on the roof for maybe 20 minutes. His estimate came back at $1,840 for "spot repairs" to a few areas. He said my roof sustained minor hail hits but wasn't damaged enough to warrant replacement.

I then had two separate roofing contractors inspect it. Both said the same thing - the hail hits are throughout the roof, not isolated, and the shingles show granule loss that will accelerate deterioration. Both said I need a full replacement, with estimates between $14,000 and $16,000. One contractor offered to file a supplemental claim for me.

My insurance is State Farm. I have a $2,500 deductible. My question is: what's the process here and is it worth fighting? And should I let the roofing contractor file the supplemental on my behalf, or does that create problems?