Yes, having helpers was the key to getting it done right :-D I'm still !ALIVE thanks to that š¤£
Our neighbors are quite complicated people, and waiting for them to remove it was of no chance. I offered to help them on their side, but they never got back at me, and the tree was in a somewhat dangerous position. So better do my side and be done.
I think I didn't post the picture as how it ended up:

The tree didn't have many leaves to begin with. I think it was already sick. The neighbor's yard is a mess. The soil there is very sandy, and it hadn't rained in weeks, plus the wind... even healthy roots have their problems with a tree that high.