I always think of jIH je as being tacked on to the end of what someone else just said. je is just acting normally as a noun conjunction. It adds the person speaking to the subject of the sentence.

That sometimes breaks the rule of rom by turning the original subject into a plural first person subject, or ends up with a redundant maH jIH je. It sometimes tries to conjoin an explicit jIH with an elided subject, which is bizarre. But ignoring the potentially wrong verb prefix and/or the unspoken first noun, I don't see anything wrong with the order of the words themselves.

-- ghunchu'wI'