I think it is wrong to read "水無月十三" with "minazuki juusan". "minazuki juuzou" or "minazuki juuzoh" is correct.

DMM agrees. http://www.dmm.co.jp/mono/doujin/-/list/=/article=author/id=25127/
みなづきじゅうぞう -> minazuki_juuzou
While plenty of references to "じゅうさん" exist, I suspect they're a nickname formed from the short version of his given name.

Wow, he even has an entry on Hatena Keyword. Whoever first decided to call him "juusan" instead was lazy enough for a report.

It's probably a nickname.