S., our speech-delayed, potty-training-resistant 7-year-old was in a similar situation as your son. It was a huge challenge to find a place when he was 3, and we finally placed him at Play and Learn Family Daycare (http://letsplayandlearn.com/) because no preschool would take him. They are in Lomita, and very warm and loving with their children, and they will assist your son in communicating. We were recommended to many preschools, and many tried their best. The one I would strongly NOT recommend is Temple Menorah. They talk a good game, but were not the least big accommodating to our son and his speech challenges.
Since you said your son is three, have you looked into the local school district options? At 3 the school district should be available to put your son into special ed preschool due to his speech delay. We live in Redondo Beach and I have heard their system is so full they don't take all students, but you should at least call and check it out.
Also, as a mom in special ed, I would investigate why your son is speech delayed. With our son they just said he was because some kids are like that. Turns out he has auditory processing disorder, probably due to multiple ear infections. He also had a mild hearing loss. We just found it out when he was 6-1/2, and if we had known earlier, there were therapies we could have started much earlier.
I know it's a challenge. Feel free to message me if you have any more questions.
Take care,
B.