For the OP, In CA, you just need a master's degree to become a Licensed Educational Psychologist, so you'd have to jump ship in Clinical Psychology and apply to a master's program in educational psychology or school psychology with regional accreditation, complete the program, work in the school system, and get licensed.
They may hire you as a school psychologist, but they will also pay you as a school psychologist. This move would potentially be leaving a huge sum of money on the table.
Not sure what kind of jobs you're thinking clinical psychologists get (of course neuropsych will pay the highest, but not everyone went into that subfield and can command that level of pay), but school psychologists in CA pay well, and in some cases, higher pay ceilings than clinical psychologists. Keeping in mind that most psychologist jobs that are posted are community mental health, geriatric settings, etc., the pay is about the same for both starting out, but school psychologists can command about $100k after 3-4 solid years of licensed practice in schools...which is a number you will rarely see a clinical psychologist position advertise unless it is related to leadership/administrative, technology-related, or a VA position. In short, $100K+ is considered very high pay for psychologists of any kind in my area (except neuropsych, of course, which required specialization).
Also, in my area, the job outlook is good for school psychologists, if the constant job postings for school psychologists are any indication. Of note, they only require a master's degree, so no further education would be necessary, at least in CA.
So for the OP, this would actually be a pretty good move for you if that's what you're wanting....especially if you don't plan on private practice or counseling extensively in your career and love assessments and IEPs/developing educational plans for kids.
If I were you, I'd start looking up pay for your area for school psychologist jobs and look at job duties to make sure it's a good fit and move on from there....