As far as the fact that the people you're hiring aren't "officially certified" experts in English teaching, my personal opinion is that you are probably beyond needing "teaching" in the standard sense. It looks as if your grammar and vocabulary are at a very high level which means that what you're looking at now is trying to sound as near native as possible, both with your accent and your use of the language. Provided the tutors that you hire are native speakers, and know good English when they hear it (and use it themselves, of course), I think you're fine holding conversation classes with them. Provided they're happy to pick you up on every bit of poor pronunciation and always point out a more native, more natural way to say something, you'll still learn a lot.
The mechanics of pronunciation are a whole different ballgame and tongue positioning etc is perhaps better taught by someone who knows what they're talking about!
When you said "My English is not as good as they say", what did you mean? What specific problems do you think you have with the language? You didn't specify.
I would disagree with the statement that pronunciation and accent are easy to deal with and that your tutors might be saying that's all you need because they're easier to teach. Accent is a very difficult area. Pronunciation is the easier of the two provided you are someone who can physically pronounce the words (and there are people who simply can't).