Ok, I'll keep playing devils advocate here.
Built in 1928 is of no relevance. When did you purchase the property and was said tree there then?
It does look rather large. At least 30 to 40 years old. I'm guessing more. Maybe it was a sapling then?
And, did you consider the possibility of actually talking to your neighbour? In a friendly way, not demanding instant removal.
I say this, because, I've been the that person that has the 'tree'. But, in my case the tree was at least 50 years old, neighbours house was 20, and pool was 2 years old. My pool was 10 years old. I knew it, he knew it. Get over it. I even offered to clean the leaves and branches every month or so myself. No, he wanted it gone. Such a shame he lost and was forced to pay costs. I tried to be reasonable.
Old neighbour sold up, new came in and loves the tree. In fact we have monthly BBQ alternating at our pools on clean up day.
I've made a great friend out of this monstrous tree.
So, I'll just throw in another
for positive thoughts