Am I entitled to see a copy of the independent claim adjuster's report regarding storm damage to my house?

Oh no.  It is absolutely not privileged, which is what the "work product" excuse is usually all about.  You have an absolute right to get a copy of the report faxed, e-mailed and mailed.  You have a right to dispute the report and the amount that they are willing to pay.  How can you do that unless you can get a copy of the report and submit it to a contractor to bid?  Otherwise you won't know if their calculations are correct within the industry.  Many times adjusters use calculations that are for prices NOT in New York.  In other words, lower calculations.  Send them a letter demanding a copy of the complete report.  Send it by fax and mail and e-mail.  Tell them that if you do not have it within 10 days you are filing a complaint with the NYS Department of Insurance.  And then do so.  Good luck.