Should the Hellenic calendar change for people in the southern hemisphere?

Taking away from the "Hellenic Polytheism Household Worship Book", the Hekatombaion, which was the new year for the greeks, starting in july, is stated to be just after the summers solstice (for the northern hemisphere, because, obviously, greece is in that part of the world). My problem is, what about us southeners? I myself am a brazilian, and in Brazil the summer solstice this year is 21st of december. In that sense, should i move the lunar months to fit my geographical location? I think that would be kinda more appropriate because the holy days are severely based on the accurate placement of the solstices and equinoces and the phases of the moon, and i do not think that the hellenic calendar used now, which pretty much only works for the north, is right to people in other courners of the globe.

But anyway, just checking out, please leave your opinion in the comments, if there are other Hellenists in the southern hemisphere i would be glad to hear what is your way of practicing the religion.