A 320-ton obelisk would require a ship of at least 400 tons displacement or 363 cubic meters displaced water. If you figure the ship was 60 meters long and drew 1.5 meters of depth you get a beam of 4 meters, so these rough dimensions aren't too bad. But I'm probably off a fair bit in only assigning the ship an empty weight of 80 tons, could be double or triple that because of balast, freeboard, decking, lead plate, etc.
Nevertheless, A Nemi ship would have been in that size range, so they were well capable of atlantic crossing.
I wholeheartedly agree. Romans used Indian elephants (from India, obviously ;') in their games, and they got them there aboard ship. A single Roman galley was bigger than the Nina, Pinta, and Santa Maria combined.