I think these plants would grow in your location. It is a little colder there, but these are hardy plantings. The blue oat grass, siberian iris, sedum, red mother of thyme, blanket flower, lavender, and maiden grass all will grow in your region. The ceanothus may be too tender, but it is worth a try. I suggest trying a plant or two to test how they do and then expand from there.

What is the purple groundcover? Is it invasive?

The purple flowers are Thymus Serphylum, red mother of Thyme. It spreads quickly from 4" pots set about 18" on center and it is not invasive.

I live on the North Shore of LI as well and have a ton of different types of Thymus, they are all doing great here, they are drought resistant and have a nice smell to them. I bought them at Martin Viette Nurseries, they carry them every spring in different types and colors.

Stunning! I love the way this looks. This is by far one of the most beautiful gardens I have seen.