There is no doubt that the person who named all the months was a genius. My theory is that before he could pen them all down he told his son or friend and then passed away tragically and this friend/son was young and daft and so he struggled with the last 4 names. That's why there's ER from Septemb..errr, to DecembER! So technically it's supposed to be Septemb something, Octob something, Novemb something but he couldn't remember so he just ERr-ed. However it is likely there is no something after Decemb and it was intended to be Decemb only. He must have been wondering about a 13th name so he wrongly for one last time ERr-ed again.
On the other hand it could be that the last 4 months are not ERrors after all and that they have EMBERS in them signifying the burning end that in this case is the year. But that is not fair to October who's stuck with an OBER (read ogre) and so is unhappily the odd one out and wants for it to get over! So yes I am content sticking with story no. 1. Even though this is not much content to be content with!