Yes, you're right. Stella Maris in San Pedro (which Apb. Lefebvre blessed and consecrated along with the chapel in Arcadia sometime in the 80's) is a Sunday-only mission chapel ever since I can recall. I don't know if Fr. Ward or somebody else says Mass there daily.
Somebody else; but not daily.
Relevance? (of it being a Sunday-only mission chapel)

I apologize, but I can't follow you...
First you said:
If I'm not mistaken (correct me), the Chapel in Huntington Beach (CA), Our Lady Star of Sea, was privately owned, and when Fr. Johnson (RIP) became ill and could not go on saying the TLM, the Chapel was taken over by the diocese of Orange.
Now today, it's:
I have no records of that or have read anywhere that's it's privately owned, but the takeover and the intention to sell is nothing more than to get more funds to pay for the pedophile lawsuits or recover the costs of the lawsuits against the diocese.
It
seems you've gone from thinking it was a privately-owned chapel--to a chapel that was never privately-owned--in just two days.

Well not without a "fight." Fr. Berry, formerly of the SSPX, put a claim that Mons. Donohue willed the chapel to him, because he had been assisting there, but actually the Monsignor did not like Fr. Berry's sedevacantist ideas (esp. from the pulpit) and Fr. Paul Tague, SSPX, took over. There was a lawsuit on this and then an election among the congregation (I was there) to vote who we liked the chapel to go to: Fr. Berry or the SSPX. The SSPX won.
Yawwwnnn... me too.