Napa’s assessor site has an example that would suggest this wouldn’t work.

http://www.countyofnapa.org/Pages/DepartmentContent.aspx?id=4294968559

Here’s another article that also suggests it wouldn’t work.
http://www.paullawgroupsf.com/articles/property-taxes-qa/

As I read both links – the transferred portion would be taxed at the new rate, at the time of the transfer. Exceptions would be if it were transfers between spouse, parent/child, into/out of a trust.