Shame he didn't know Portuguese then… http://www.learn-portuguese-with-rafa.com/days-of-the-week-in-portuguese.html
I was actually very surprised when I found out that Japanese has names for each day of the week when the months of the year are simply numbered. That reminds me, the reading for 月 used in the month names is unique to that context, I think, so I suppose that could be translated as "month of the year."
It seem to be easier that the french-based names! IMHO, the best template of it is [Number]semajnero (semajno = week, -er- = the suffix means a part), E.g. lundo (Monday) = unsemajnero (the first day/part of week); dimanĉo (Sunday) = sepsemajnero (the seventh day) or lastsemajnero (the last day). But such names make esperantists from countries, there week starts on Monday, misunderstandable in countries there week starts on Sunday and v.v. I think esperantists won't accept such ideas while there are the diffrent orders of the days.
Yeah Chinese is similar to Japanese in its simplicity. Monday is zhouone, tuesday is zhoutwo... Zhouthree, zhoufour, etc. works really well. Months are the same- Onemonth, twomonth. For the date they say onedate. So for example, today is Friday, January 29th. In Chinese you would essentially say. Today is zhoufive. Onemonth 29date. Much simpilar. I understand Zamenoff only had languages he knew to go off of and he probably didnt have much exposure to Chinese. However, that guy up there saying it wouldnt work because using numbers in dates doesnt sound like a natural language is just plain wrong. Chinese and Japanese do it fine.
The meanings of 初, sho- is beginning, start and first, but you're right, it's only first, really, because that's what a beginning is.
That said, however, once you call the first of something sho- it still makes sense to continue with numbers, shogetsu, nigetsu, etc, same as shodan, nidan, etc for martial arts black belt ranks. Calling the first of something sho- doesn't imply another system but numbers.
If the months followed another system, the first one would also more likely have a different name, and it used to: mutsuki, followed by kisaragi, yayoi, uzuki, satsuki, minazuki, fumizuki, hazuki, nagatsuki, kannazuki, shimozuki and shiwasu.
No numbers in sight – well, apart from May, where satsuki is basically an alternative pronunciation of exactly the same characters as gogatsu.
october as 10th month is due to the fact that the year would start with spring, in march (until 1582 with the julian calendar). then september was the 7th month, october the 10th, november the 9th and december the 10th since those words come latin and are common to the latin languages.