New At Hiking,
What you are talking about is called a slack pack in which you start at one end with a light pack of just what you are going to eat, water, first aid kit, and maybe something to put on when it rains.
To begin with, your numbers are wrong. It is about 16 to 17 miles from Len Foote Hike Inn to Three Forks. The approach trail is not included in the AT miles, so you are correct with the AT miles.
It would be good if you have your crew meet you at the FS42 Parking lot after you summit Springer to see if you feel up to the next 7 miles. All the difficult miles are up to Springer, the rest is a breeze. So, the driver if you are feeling tired could meet you down the trail at Three Forks.
But you should have a bail out point at the mid point to make sure you are not too tire. There is a Forest Service Bulletin Board at the parking lot at FS42 where you can leave a message for the driver to meet you at three forks if you wish to press on and the driver is not there yet. Have fun.
Mr. Boo