If you actually mean accents here, then I am not comfortable with the idea of more or less neutral if I don't have a neutral base for comparison.
And we still seem to be playing with the same difference of opinion about definition of terms. For me, average, generally accepted, generally accepted as neutral, etc do not mean neutral.
Now that you have clarified it, fine.
It still appears to me that you have made a jump from phonemes to geolect. Suppose we found (and this is a purely hypothetical idea) that you and Ray pronounced the diphthongs in both die and day differently. Suppose further that 99% of people surveyed thought that your pronunciation of die was 'close' to theirs, but that Ray's pronunciation of day was 'close' to theirs.
Are you suggesting that a 'neutral' accent would have in its bank of phonemes your /aI/ and Ray's /eI/?
Surely. But there are many of them, and when one is honest, one finds there are a few favourites people prefer to hear. The Black Country on the outskirts of Birmingham, for instance, is so hard to understand by non-Brummies I feel sure few would select it from a list as an accent they found neutral, standard, easy, elegant, useful, etc.