Hi there, 

When you click into the NJ extension "Sent to State" status, is a Submission ID displayed?

If so, it sounds like the extension was transmitted, so you'll need to wait for it to get rejected (assuming that it will for the missing signature date) in order to retransmit.

Is it possible that the "Not transmitted...not successfully converted" message related to an earlier attempt, or different agency's extension? I wouldn't expect a return with that message to then show as Sent to State.