See, it does not matter whether you have appeared for the Joint Entrance Examination, Advanced when you first cleared your class XIIth examinations. According to the rules, if you have cleared class XII exams in 2021, and you have not appeared for JEE that year, it will still be counted as one of your attempts. And if you'll not give in 2022, still it will be counted as your second attempt. So, you have exhausted all your attempts, and changing boards will not help you as you can give JEE Advanced only two times in you lifetime.

Hope I have answered your question. All the best!