Hi,
Our Agapanthus are planted outside here, and they get the miinimum attention. We get frost where temeratures fall to about 6°C, but this does not happen every day of winter though. The plants only get compost as fertilizer, and they get watered whenever they seem to be slightly stressed.
I would still overwinter it in the pot if I where you, don't just overwinter the bulbs. Maybe cutting back a little on the water given to the plants will stimulate them to flower.
Why don't you pot them in a nice looking pot and treat them as potplants, keeping them indoors permanently.
SAVeg

SAVeg, does it really only get to 6 degrees Celcius when you have frost? meaning that it never freezes?
Last winter was our first in this southwestern Oregon location. we live at 1500 ft elevation on the north slope of a 2500 ft mountain, and temps dropped to 14 degrees Fahrenheit (that's wayyy below freezing) for a solid week on our deck where my agapanthus spent the winter in 5-gallon containers. They overwintered well and bloomed profusely all of July and August, but i bet that it would have killed them if that cold spell lasted another few weeks. My plants have been in the containers a bit more than two years now, and are rather potbound but apparently happy.
All i know about New york's weather is that it gets much colder than here ... perhaps a good idea to post your question on the forum frequented by other New Yorkers, and ask if any of them has success with agapanthus. A. africanus is not regarded as a very cold tolerant plant.