Problem solved! Aristos stated the problem exactly, and to fix it and keep the original functionality unchanged, I replaced the Refnum with a string in the private data, and in the accessors I added code to flatten and unflatted from string. Thus the refnum is still stored in the class, and no code outside the class had to change, and I was able to hide from LabVIEW that ugly strict refnum it seems to hate so much.
I would still like to hear why this is a problem, and, more importantly, why it is not stated more clearly by the compiler or the application builder. I want my two days back!
George