Robert has it right. 356COUPE posted some info that needs correcting. The "normal" process he refers to above is illegal. The only legal way to register a 356 replica in California is by using the SPCN specialty construction registration method, irrspective of whether it's on a VW pan or tube frame. To register a replica as a VW if it is no longer recognizable as a VW is a violation of the CA Vehicle Code Sec. 580. Many replica owners have followed this method, as it's easier and, not coincidentally, cheaper.
I registered a TN replica in CA in 2013. I had a few glitches, but completed the whole process in 2 working days. For the past few years, the 500 SB100 SPCN permits have lasted at least through August, so the backlog seems to have abated.
Google is your friend. Do your own research. Don't take one person's word as gospel. After researching several sources, make a registration decision that works for you.