I do track events at Sonoma/Thunderhill/Laguna Seca with the follow groups (in order of preference):
Golden Gate Lotus Club
I know the groups you're talking about. NCRC is one of them. They're a bit pretentious about who runs with them, but they've let me run in the past. Just today I reached out to SpeedSF about letting me run with them. There's a third but I forget which it is.
In general I understand some groups' reluctance to let hot garbage out on the track. A lot of groups will black flag a whole group if there's a breakdown, which kills time for everyone. So if you have a total heap they don't really want you out there. Likewise if you're a total newbie signing up for open passing right away. Or hella slow trying to run open passing with much faster cars. But I think if you reach out and explain that you're not a knuckle head, there's a decent chance they'll make an exception.