I had two previous cello techers before I found my current one. He was recomended by both my sister's flute tescher and my school string techer (all those music teachers know each other). So that is one good way to find a good one. My teacher is brilant.
I've given this some thought now as to why I think he is such a good teacher and I've come to the conclusion of;
The students self confidence is a huge factor in whether or not they will progress. If the teacher (like mine) will tell you that what you are doing is wrong, they will also say what you are doing that is right. It could even just be that your posture is good or you have a nice hold on your bow. These little thinkg relly do have an effect on your self-confidence which in turn effects how much pracice you do and so your progress. My first teacher on the first lesson pretty much just bagged everything about me, my playing ability and my actual cello! Her main instrument was violin, not cello too, which I don't think helped.
Another good thig about my teacher is that he does care about me and my progress and isn't 'just in it for the money'. This is simple to see by the fact that because I'm his last student on that day he gives me a 45 minute lesson instead of 30 minute lesson which is all I had paid for. He is willing to give part of his time and family life away to me for free. another point I'll make her is that tomorrow night my highschool is having an extension music concert. Geuss who is going?
I noticed that you mentioned teacher X's qualifications. Just remember, any acedemic in music can go to uni and get these. That first teacher who I mentioned before had a B. mus and B. edu she was a hopeless teacher though and was quite expensive because she had these qualifications. My current teacher has these qualifications too I might add, but my point is that don't rely on them entirely. That is what I had done. I too have done grades on pinao, before I started cello. My piano teacher was recomended by my best friend who was at that time quite high in the grades. She had no qualifications in music or teaching what-so-ever. Yet, she was a brilliant teacher. Her day job was as a secretary. She just taught piano from her home in the afternoons. See what I'm saying?
But, if I can give you, or anyone just one bit of advice when trying to find a good teacher is this; try them. There is no harm in doing so. If you aren't learning or progressing by their teachings and they have tried to explain it or show you it in differnet ways (if they are able to, this would be part of the test) then try another teacher. Trial and error. the way many great things have been discovered. That and by accident off course.
Good luck my fellow musician. Let us know how it all turns out.
(and sorry that this is so long. You should feel honered that I just sat here, thought and then typed all this for you.
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<Added>Oh dear, please excuse the errors through this. I've had a long day.