I don't think it'd be odd for the initials to be in the centre, for that time period .... they were proud of their monograms. Often times it was on pillow case edges, and other linens, in full display. Also the centre initial as the last name, was usually larger, more pronounced, though with the little "c" I vote for the last name ... so that'd bring you to NJNc for the initials now.
Also, for olden times, the maiden name was not uncommonly used as the lady was yet to be married and was making things to use at the time. So considerations to the maiden names might be made.
Names often did get changed ... hiding from familial ties was one. Also, how it was entered into Census Records and as already mentioned your entry point at Ellis Island. So it really isn't a stretch that it was Nc .... and from that other link, looks like they may have got changed from Nc to Mc too!