Yes, CEP will apply and HR will assess your current subgrade by estimating your remaining runway before retirement.

Also, to answer an earlier question, P8 (GEO5) is the lowest CEP one can get. That said, it also means reaching GEO5 before retirement, which is why you may still be at GEO3/4 after many years. For those that reached GEO5 relatively early (within first 8-10 years), that is because the school likely raised your CEP to P7 (SEO1). This coupled with your performance grade will determine will determine how early you eventually reach your end-grade of GEO5.

I think diploma vs degree plays a part too, but less so these days due to a shift in the mindset of public service.

Would also like to point out that ultimately, CEP determines your rate of promotion (with consideration to performance grade), not performance grade. A dedicated and capable officer can get C+ and B each year but have a CEP of P8 or P7. When selecting MMs, they need to be good people manager (positive influence), ability to lead and also good situational awareness.
Of course, they are expected to have certain baseline pedagogical skills still.

There are some teachers that are really good but are either contented as HOT, or just not careful with how they nuance things or cannot speak well. I know a really dedicated science teacher who applied for a HOD position in another school, but he is not confident to speak up in front of all teachers and dare not raise his views in groups.

Last, luck always play a role when it comes to promotion. Are you in a school where there are many bright stars shining? P (and Supt) would likely highlight a few names to HR, not give a long laundry list. I was in a school that had two overseas Teaching Scholars (HR would highlight them and school is expected to provide them opportunities for growth) and we are part of a batch of more than 15 teachers entering the school in the same year. Things really got a lot better for me when I went for my next posting. A chance of environment can help, which is why many teachers I know would choose to look at posting somewhere else (even HQ). It also broadens your perspectives, which is useful when considering someone to take up larger portfolios.

That said, if you are not happy, do speak to your RO and SLs candidly about what your AFIs are at the very least. Our AFIs are usually our blind spots. That said, nth stopping you from finding success outside of MOE. I am however always sad to lose good teachers/colleagues to the private sector, or other ministries.

Best of luck.