Adjuster says my hail-damaged roof is only worth $4,800. Three contractors say $22,000. What now?

Had a pretty brutal hailstorm come through our neighborhood in March. My neighbors on either side of me both got full roof replacements approved. I filed a claim and my adjuster came out, spent about 20 minutes on my roof, and gave me an estimate for $4,800 to "repair damaged areas." Three separate roofing contractors I brought out all said the roof needs full replacement and gave estimates between $19,500 and $24,000. One of them pointed out the adjuster's report has the hail diameter listed as 0.75 inches when actual weather station data shows 1.5 inch hail that day.

I've been a customer with this insurer for 14 years. I've paid my premium faithfully and never made a claim before this. The fact that my neighbors got replacements and I'm being offered a patch job for a fraction of the real cost feels wrong to me. Do I hire a public adjuster? Try to negotiate directly? Is there an appraisal process I can invoke? I don't really know what my options are at this point.