You cannot use any reference to the class itself within the class. Technically, we could enable some things, like a DVR of the class within the same class, because the default value is Not A Refnum. But we chose -- consciously -- to make the rule "no references to yourself in your own private data." It's an easier rule to teach, and it has various performance benefits for initialization (that mattered more on the hardware from 13 years ago than they do today). And it has come up very rarely. In fact, I think you're the first person whose asked me specifically about the VI reference case. All the others have a reasonable workaround... need an array of X? Use an array of its parent class (which may be LV Object). Same trick works for most refnums... or you can always cast a refnum as an integer and cast it back when you need to talk to its data.
But casting doesn't work on strict VI refs and you cannot use it as its parent class type.
I think you're stuck. I can't see a way out of that box.