Hi E.,
You can't go by advice from non-CA moms -- every state has different funding and legislation on this matter. I'm not sure what the law says now, but when we moved our daughter from public to private school in the Los Angeles area (LA City Schools) in 2004, we lost our right to speech services. As I recall, this was mainly because speech is a pull out program that requires the child to have access to the therapist at the public school. Neither the private nor the public school was allowed to provide transportation, thus the services could not be delivered during school hours. I'm not sure if we could have had services if we had shuttled our daughter back and forth, but we weren't able to do this anyway (I worked over an hour away and my DH was in graduate school at the time). We couldn't afford both private school and private speech therapy, either, but we did find that Cal State U Northridge offered speech services at a cost that was the fraction of the cost of private care, and they offered evening services that we could work into our schedule.
I would check with the district office of whatever public school district you're in. They will be able to tell you what your options are, if any. If you have to get private speech therapy, check out the local universities, and see if any offer speech services at discount prices -- but do understand that your child will be seeing a student therapist under the direction of the professorial staff. At the time, CSUN had one of the best speech therapy schools and treatment programs in the country, although I understand that's changed since so much funding has been lost.
If the only option is to stay in public school to receive the speech services, personally, I would stay with the public school until the speech issues are resolved. You can supplement your child's education at home if need be far more economically than you can paying for speech services, and those speech skills are not only essential for later success in school and career, but can also make a huge difference socially. My daughter had a difficult time making friends for the first couple of years of school until her articulation improved -- the kids simply couldn't understand what she was saying, so it was very difficult to build relationships.
Good luck!