Re: July and August must Go!
Dunno about the "proper" Latin names for an eleventh and twelfth month, but this may be of interest to calendar pedants :
(As part of Julius Caesar's calendar reform, two months were inserted between November and December in 46 BC. "It has been suggested that their names were Undecember and Duodecember, but that is doubtful, as this would mean that the names of the last four months were derived from the Latin words for nine, eleven, twelve, ten – in that order." Note that this was a one-off event; the Roman calendar required occasional leap months, but that hadn't been done for a while. The extra two months were to get things back on track.)
So... JFMAMJJASONUDD. But if we wanted logic, we'd have switched to the French Republican calendar.