I find the reaction to the advice being provided to be curious. It reminds me of when my children present me with a problem and no matter how hard I try to problem-solve with them, brainstorm, address their stated concerns, etc. they just respond back with "YOU DON'T UNDERSTAND!!!"
I am hearing you consistently assert that the level of respect, autonomy, and integrity that you experience working as a school psychologist is limiting and frustrating, as are the poor working conditions. I get that. I foresee it getting worse (DeVos's appointment today does not likely bode well for public school employees or special education services). Good on you for recognizing this situation and taking steps to change it. That is an honest and courageous move.
I am hearing you consistently imply that you do not want to invest time and money in a new/different career direction to end up unhappy again (smart!)
I am hearing you report a series of experiences and personal preferences that suggest that you may not find the happiness/satisfaction that you seek working in another client-based, helping profession. Moreover with recent proposed changes in health insurance, private mental health insurance coverage may be reduced for a portion of the population and another portion of the population may fear using insurance coverage for fear of establishing "pre-existing conditions." This may deplete the client base and increase insurance hassles.
You might want to look at any/all of these factors and use them in your decision-making process.
FWIW, I spent AN EXTRA several years in grad school to complete a school psych PhD. program in addition to the clinical PhD. program that I was already doing. That meant extra time, extra debt, and extra loss of income. I then chose (for various reasons) to parent full time after completing both PhD programs. Ironically ALL THREE of my lovely children have special education needs, so in addition to my clinical and school psych training, externships, practica, internship, etc. I have had the real-world experience of serving on teams in multiple public and private school settings, therapeutic day schools, etc. in addition to working with countless private therapists. After all of this unpaid experience, I too have concluded that working as a school psychologist in a traditional setting would not be a good fit for me. It would be much easier for me to pursue that role at this time as I am certified and could go out and get a job tomorrow. Instead I am studying for the EPPP and searching for a postdoc so that I can complete my licensure and continue down a clinical path (which means more time, money, and loss of income in the process, not to mention that the extra years I spent on the school psych degree are a wash professionally). It's not an easy choice, but I believe that it was the right choice for me in the long-run. Good news for you, you got to do all of this self-discovery while earning a salary. I was not so fortunate.
I am not in any way diminishing your experience, your conclusions, or your desires. I find many of them very relatable. That said, if you are at this crossroads, it seems to behoove you to look carefully at the next path that you choose so that you aren't likely to find yourself singing the same tune on a different stage in 5 or 10 years.