I did the reverse, starting up towards the AT from Big Creek, and cut over on the Balsam Mountain Trail to the Benton MacKeye. I was with a group going at a leisurely pace and it was 4 days / 3 nights. A longer alternate would be to use the Hughes Ridge trail to go between the AT and the BM.
We really liked the less crowded BM trail a lot more even though it didn't do any ridge running, and with Sterling to Big Creek being so steep we were happy to be going down that section rather than up. There were a bunch of AT thru-hiking people on the AT, the camping sites were very crowded, and more than one person gave me and my buddies grief for out pack weight and size (we carried in fresh veggies for huge meals, non-lightweight gear, etc). It was kind of obnoxious. The Mt. Cammerer tower was definitely cool. Anyway, the NPS map was a great planning tool (google GSMNP trail map)
I should add that coming from Pennsylvania, starting in the northeast section of the park cut down on the drive time considerably compared to Balsam Mountain or Smokemont (the southeastern entrances to the park).
A day in Asheville to recover and eat / drink well was fun & recommended if you have the time.