Scrap months altogether, just divide the year into quarters of 13 weeks each, name them for the seasons, Winter, Spring, Summer, Fall, there isn't really a reason why we need months specifically, if it's to shorten date numbers then count by week number and day number
Nothing stopping the other half from just flipping it to match their seasons, that's what they do already, and the number for date stays the same anyways
I work and converse with people globally, as much as I love the idea of being able to use seasons as a marker of time like that, it's just not possible.
Onzember based on how the last few months starting with September are all just part of a number in Portuguese/Spanish (and maybe other languages) + ember. Ex: November = Nove + ember, Onzember = Onze + ember