State Farm denied my water damage claim citing the 'gradual seepage' exclusion but my plumber's report explicitly states sudden failure of a copper supply line. How do I force a re-inspection with their engineer?

Came home from a 4 day trip to Colorado last weekend and walked into about 2 inches of standing water in our finished basement. The cold water supply line going to the upstairs bathroom (under the second floor, runs through the wall and ceiling cavity above the basement) had failed. My plumber pulled the section out and showed me a pinhole on the inside of an elbow fitting. He said the elbow had thinned from the inside out due to a manufacturing defect or water chemistry, and the failure was sudden because the line was holding 60 psi until it ruptured. His written estimate and damage report describe the loss as "sudden and accidental rupture of a copper supply line fitting." Total damage estimate from the water mitigation company is around $38,500 for tear out, drying, and basement reconstruction.

State Farm's first adjuster came out Tuesday. He took photos, spent maybe 40 minutes on site, and called me Friday with a denial. He says the water staining patterns in the ceiling above the failure point indicate "long-term seepage over weeks or months" and that the policy's "constant or repeated seepage" exclusion applies. He also said the elbow fitting shows "internal corrosion consistent with gradual deterioration" which he claims means the loss was not sudden. Total approved amount is $0. Deductible would have been $2,500 anyway but they want to deny the entire claim.

My problems with the denial. First, the staining he is calling long-term seepage is the actual damage pattern from when the line ruptured and water cascaded down through the ceiling cavity over 4 days while we were gone. Of course there is staining. Second, internal corrosion of copper elbow fittings is a known industry issue caused by water chemistry and is exactly the kind of latent defect that produces a sudden failure when the wall thins through. Third, his entire denial is based on his visual inspection without any engineering testing, sampling, or laboratory analysis of the fitting.

I have the failed elbow fitting in a labeled bag in my garage. My plumber kept it specifically because he expected the carrier to push back. What I need to know: how do I demand a re-inspection with their engineer (not just an adjuster), how do I get the failed fitting tested by an independent metallurgist, and is this the kind of denial where I should hire a public adjuster immediately or where the threat of a public adjuster will move them on its own?