Welcome to the RTA forum!

Your visa issue is the one that seems like a pretty big potential issue. Basically, are you certain that you will be eligable for a tourist visa, 2 days after your work visa expires? That is something I'd make absolutely sure of, since you wouldn't want to be stuck in TJ without a way to get back to the US.

Getting a car licensed and registered shouldn't be too hard, since you've already got an address in NY that you can use for the paperwork.