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My contractor met with the insurance company and explained why their
estimate was off. The insurance company agreed and paid me the higher
value. You "should" be able to get them to do it also. Maybe I just have
a good insurance company (OneBeacon) but I have found them to be very
reasonable over the years.

As someone else pointed out, the high deductible was your choice; while it
might be callous, you really don't have a right to complain about that
now.

Good luck in dealing with the insurance company.

High deductible? That's the lowest you can get. Most Floridians have a
$10000 deductible