In NJ you definatly can not register as a moped, the engine size in CC's is to big, it goes to fast and has no pedals.
While investigating titles in NJ I was directed to the Foreign Title Unit, 1-888-486-3339.
If you call them and tell them you have a garge built motorcycle they will send you out a "Title Kit" which is mostly state rules for all kinds of home built or reconstructed vehicles. But included will be a
SS-7 form and a SS-143 form and a check list of doucuments you need to provide to get a title.
I have not done it yet but it seems you mail all this in first and they then mail you back a reconstructed title.... my only fear is they want you to send originals of things like your MSO of to who knows where?