There's a pretty big knowledge gap in understanding the structure of the spire right now. We don't know much about the interior structure on the vertical plane where the spire met the main roof (i.e. the lower north side of the spire). There was likely some form of arch there, at least as big as the main exterior door arch on the south side. If there was a pair of column-type structures there on the north side (similar to the two southern corners of the central tower), the initial failure may be the northwest lower column of the tower, with the roof level buttresses being more for lateral support than vertical support.
I spent a while trying to find interior photos which might show some detail looking south towards the central tower, but didn't find anything useful. I was searching based on "First Church of Christ", "First Congregational Church" and "Engaging Heaven Church"; the first two terms match a lot of different churches, and Google's image search engine doesn't seem particularly good at narrowing it down to just the New London church.