Cymbidiums will be a challenge to get them to bloom where you are so if you want to try one, make sure it is a warmth tolerant variety. I can tell you that a species that does really well for me in the Keys is Cym finlaysonianum from SE Asia. Warning, like a lot of Cyms, it can get pretty big.
You should do fine with just about any Oncidium or allied species and hybrids. They are pretty forgiving and again, ask about temp requirements as well as light, water, etc.
I don't see Epidendrum or Encyclia on your list. Most do well where you are and some maybe even native to your area of the state. If I may be so bold, try and find yourself an Epidendrum ciliare. Preferably mounted as it presents the flowers better and is a rambling spreader. The blooms are fair sized, white with a lacy lip and the evening fragrance will be intoxicating on your lanai.
I have over 200 orchids and it is absolutely one of my favorites.
Also, I don't know what type of vanda you have but if it's doing well, I would also highly recommend any of the Aerides or Rhynchostylis species. Grown just like a vanda and they have bright colors and lovely fragrance.
Let the IOSPE be your friend in exploration.
http://http://www.orchidspecies.com/#sec1