Hello. As far as I know,月 is a simplified form of 肉 and the character originated from 甲骨文小篆.肉 exactly refers to human body.For instance:脑,脸,腮,肋,肚,肝,肛,肠,肿,脂,肪,胆,脉,脯. You got it right.In Chinese,usually the meaning element on the left and the phonetic element on the right.But in some case the meaning element could be beneaththe phonetic element,e.g.腐,背. 月 in general could be related to human body,but in modern Chinese,it could also refer to the moon,for example:明,朗,朝,期,朦胧.

If you really want to comprehend deeply how "Chinese characters" generally constitute, you'll have to refer to some profound books such as "說文解字" (Shuōwén Jiězì), but I'm afraid that perhaps you won't understand what those explanations mean, if you don't have a great knowledge of Chinese language. http://www.gg-art.com/imgbook/index_b.php?bookid=53

This isn't an answer, but I just want to say this is a great question! This is type of Chinese I should be learning! 呵呵。 Thank you for the post Rose!

long long long time ago ~~~~~~~~~~~~~~~~~~~ , chinese yue "月" it means "meat" " rou" "肉'' ie : “肝” liver “肺”lung “胃”stomach“脾” spleen