@Imperial, You don't need to chase around Cobra sites or other 'kit car' sites. The info you need is here on this site. You can click on 'search' for "SB 100", it has been covered many times. Or, just go to the link @Theron provided because it summarizes the whole process: The Magical SB100–Registering Your Car In California – Bauer Ltd
The point that has been made for you in posts above is that you won't be able to register a 1992 anything in California unless it passes current smog regulations. And, as pointed out to you, that will be virtually impossible in your case.
So your option if you want to register in California is to go the SB100 route. SB100 was created specifically for situations like this.
I did the SB100 process about 2yrs ago on my Spyder. For 20yrs I'd been driving it around registered as a '69 VW based on a registration and VIN lifted from a 'salvage' bug chassis. Obviously the Spyder didn't have anything in common with a '69 VW so when it came time to sell the Spyder I wanted to eliminate any 'shade' from the registration and title.
Given that my Spyder was a "specially constructed vehicle", like your Beck, SB100 provides the process allowing legal re-registration and title into the pre-smog era. (which will be a registration and title that I believe is recognized and can be transferred in all 50 states, which naturally adds significant resale value to the vehicle.)
Edit: As far as being a crapshoot for who you get at DMV etc., my suggestion is to read-up on the process as much as possible so you can guide them (politely) of your 'understanding' if you feel they got lost (DON'T tell them how to do their job). Be aware in advance your DMV person is probably clueless. Also be aware (in my case) that the first step in the process was surrendering my existing registration and title. So dont start if there is any doubt you can finish. If you fail along the way, you have NO title.