There is no reason you can't register and document the boat
We live in the US Virgin Islands
and have registered several sail boats without an agent.
However... You need to register the boat
in person at DPNR. Be prepared for anywhere between 20 minutes to 2 hours. Also, be prepared for more than one trip to DPNR if you don't have all the documentation
properly signed and notarized.
Our experience was 'be polite and patient' at DPNR and it was an easy enough experience.
USCG Documentation was pretty much a matter of following the instructions on their website.