Three or four part-changes is definitely the way to go with the ATF, the new fluid will be much thicker and the "seal swell" in the old fluid will have worn away, potentially leaving the seals dry and brittle. Introducing the new fluid gently this way gives the seal swell time to recondition the seals before it gets all new fluid in and allows them to become flexible again so they don't get popped by excess pressure.
Usually the 3rd part-change is the charm but i often do the 4th one as "confirming" all the old fluid is gone. I would strongly recommend Carlube ATF-U having used it many times (similar to Dex III) on AW boxes (and a few ZFs, not to mention Honda FWD boxes that can't use Dexron
) as it meets JWS3309, the original fluid recommended by AW for their boxes.
After doing 3-4 part-changes ~200 miles apart, do one part-change a year/12000 miles to keep the fluid as it should be and you'll be fine.
