I had a red one exact same.
Suck it up and be patient, and go with the horrible DMV process is my suggestion. You already said you got it for little money. Reason: title issues. Around here it would sell for 800 with a title. Figure title issue costs and you probably got a deal.
They are a little slow but very reliable. I liked it because it was quiet.
FYI . wrong forum it is a scooter, not a moped. (edited)