I read the very interesting article you posted the link to, and found that although concise and accurate it was incomplete in some areas.
Like the fact that it mentioned that the years were firstly divided into time segements ruled by the moon. It says that the problem was that the lunar months were not a set, regular amount of days and did not divide evenly into a year.
That was not the problem.
For centuries man measured time, and many other things, by the cycles of the moon. Then came the time when people wanted to write it down and record it. Then they wanted everything to uniformly fit into how they wished to percieve time and it's passage across their lives. When man measured time by natures clock, everything was fine, but when man decided that natures clock was no longer accurate enough and tried to manipulate it to fit, they found that nature doesn't work that way. It doesn't bend to the whims of man.
That was the problem.
The fact that we now have one extra day every four years at-*test*-('")s to the fact that they have never yet found a way to force nature into doing what they wish.

I believe it is possible that the New Year would be celebrated in the 8th month, (or as you say October because it relates directly to the number 8), because 8 is the universal symbol of infinity, an eternity of possibilities, of new life and rebirth.
One more piece to try and fit into your puzzle Zygopterix.

Lastly I agree with your dividing of the year. New Year at Samhain for those things that are made by the hand of man yet honour the Mother, New Year at the Winter Solstice for everything created by Nature, and, I assume, New Year in January for the rest.
I believe that to be an excellent way of working things so that all three sets of equally important, (man to itself and nature to everything) things have the right greeting on the right day.