UPDATE
I received this response from the Int'l student coordinator at Cardozo.
(I am a Canadian currently in the US on a paid internship J-1 Visa):
If you plan to continue to work for the J organization that is sponsoring
you, you can attend school and you will not need an I-20. Your primary
purpose in the U.S. would be to be a J-1 worker for the organization. If
you choose to also attend school, this would have no effect on your J-1
status.
You only need to obtain an I-20 and F-1 student status if you plan to be a
student in the U.S. as your primary objective. If you will not work for
the J-1 organization and you want to attend school, you will need to
obtain an I-20. F-1 students must be full-time to remian legal in the U.S.
For immigration purposes only a full-time graduate student is one that is
registered in 9 or more credits. The part-time JD program requires
students to register for no less than 9 credits so you can therefore be an
F-1 student in the part-time JD program.
You must keep in mind that F-1 students are not allowed to work, so you
will not be able to maintain your current employement as a F-1 student in
the U.S.