In this design I am aiming for max 7 bit accuracy
which you will not get since this is the tolerance for the A/D alone and there is no way in hades anyone can make the rest of the design perfect.

Another aspect is that with 3k samples/sec you will sample the AC in 30 'slices' ~ 3% of the width so the max measurement will be 0-3% off the peak amplitude. and 3% of 256 being 7.7 will give you another 2-3 bits of error.

Erik