Your situation sounds quite similar to mine, jcharney. I usually dream in third-person, almost as if the dream is a video game. Scenes change spontaneously, events flow into each other without much logical or causal connection, and things only make sense until I wake up.
But I had my first LD last night, and it was sort of a hybrid POV. I seemed to be in first-person, but I had some sense of third-person-ness. It was weird. Once the dream started fade, that third-person aspect totally shut down and I could only see through my dream eyes.
Don’t not expect to have success. Even though you may have to wait weeks or months for an LD, tell yourself every night that you WILL have one. And completely believe it, too. Placebo effect, you know.
Good luck!