Still working on the situation--I won't hear more for at least a week or two because of the holidays and COVID-19 issues (big here in downstate NY), but I will say that the insurance company wanted to see copies of the certified return receipt notices with his client's signature on them as proof that I had contacted them. I have seen a few threads here poo-poo the concept as proof of nothing, but in this case it was at least proof of my having mailed them something, on more than one occasion.
Also, since a problem with a neighbor a few years ago I make a point of taking pics of my yard periodically--showing among other things the health of the trees during spring, summer and fall. This has turned out very valuable as they also wanted pics of the tree as proof of height and that it was living before cut down.
Digital pics are free, I advise anyone with close neighbors and close trees do the same! I also included some google map street views but the quality is poor, but if you haven't taken pics and run into trouble it might help.