When deciding claim is covered in writing, can the coverage later be denied?

The shorter story: I filed a homeowners claim for wind damage to my roof. The company sent a field adjuster who then sent a response letter admitting the incident was covered by my policy but the estimation of damage was poorly done because he apparently didn’t understand the industry standards for fixing the damage.

I sent an email addressing various deficiencies in their estimate. I was shifted to another claims adjuster. Then after asking him questions for months I was sent to a third adjuster.

She ordered an engineers report, after which she sent me nearly the identical letter admitting the companies coverage of the claim but including a deficient scope of damage. It referenced my policy with a few exclusions.l, however it didn’t mention any denial of claim: the scope of repair was just not complete.

After looking through all my insurance papers I couldn’t find that we ever had a hard copy of the policy. I emailed her requesting it and got a response that she was no longer the adjuster on the claim. I called back multiple times and finally got someone who mailed the policy and endorsements to me because that’s the only way you could get them.

Then, a fourth adjuster contacted me. After we talked she said she understood why I thought the damages described in the two previous letters were inadequate. She was going to check with her manager and get back with me.

A few days later she calls back and gives me an update about some things we discussed AND that my claim was being sent to their legal department because somewhere it says I have to make a claim for wind damage within a year and mine was a day too late for the dates they had in their file—basically they’re deciding after almost 2 years, 2 letters admitting the claim was covered, and 4 adjusters, whether the claim is excluded by this line about making the claim within a year.

Haven’t they decided this question already?

Also, I don’t know if all homeowners policies are like this, but it really bugs me that I don’t have a physical policy and you can’t get one on their website. You have to call and ask. But not just that—because every person you talk to says your policy is available on their website, when all that’s there is your dec pages. You actually have to know that it’s not there and demand that they send you the policy. The one-year claim date for wind is apparently in the policy language, which you can’t see unless you get them to send it to you and even then it’s buried.

What if anything can I do to help them decide this issue in my favor?