Joyceg, maybe the privet "knows" it shouldn't be there, or is trying to go home? It is frustrating when something with a reputation like that won't grow when one tries. I've had obedient plant die before, supposed to be a horrible take-over plant where I lived at the time.
The term invasive has 2 meanings. The first is any plant, native or otherwise, that's too exuberant to behave properly for most peoples' tastes in a cultivated setting. The other use of the word is to indicate plants of foreign origin that out-grow natives or otherwise take over and/or alter large portions of natural settings. It doesn't necessarily mean that individual plants are sure to live in any situation.
I've actually put some serious effort trying to gather advice for propagating Eucalyptus (polyanthemos is the one I have) but every source I could find said it doesn't work, seeds are the only option. I'm sure it's technically possible, but could find no success stories or solicit any on forums. So no need to feel like you messed up on that one! Does your tree make seeds?
Sorry I don't have any more specific suggestions, never been to CA. Any neighbors/friends who might let you snip a few things?