Why does electronegativity create a stronger acid, but so does greater electron distribution?
The main point about strong acids is ‘how stable is the conjugate base?’

The better stabilised the negative charge on a conjugate base of a neutral acid is, the happier the species will be to loose a proton and thus the more acidic the proton is. All of the points you noted just emphasise that.

Therefore, the only wrong assumption you are making is:


  more stable base = weaker acid.


The correct way is:


  more stable base = stronger acid.