‘…you need to use parentheses so there is no confusion with the root accidental, i.e. Ab6 or A(b6).’
A(b6) is ambiguous because the sixth always is. At least the sixth is defined - AC#EF - but this is F augmented fifth, major seventh, first inversion – F(aug5/maj7)/A.
Ab6 is even more ambiguous because the sixth isn’t defined.
You mentioned that an unqualified 7th is always a minor 7th…but what is an unqualified 6th - major, minor, augmented or (admittedly unlikely) diminished?
AbCEb with F,Fb or F#.
If AbCEbF it is F minor seventh, first inversion – Fm(m7)/Ab
If AbCEbF# it is Ab augmented sixth – Ab(aug6)
If AbCEbFb it is (enharmonically) E augmented fifth, major seventh, first inversion – E(aug5/maj7)/G#