I'll be doing a 4 day GA AT shake down hike May 3-6 in prep for a SOBO thru hike starting July 1. I like your plan to end at the Lodge. Never stayed there but I've heard it is very nice.
Shuttle: You may want to start with the Lodge and see if they offer a shuttle service and will let you leave your car on their property while you hike 800-573-9656.
I used Joyce and Sally last June for a section hike from Springer to Unicoi Gap.
You can park your car at their house in Hiawassee and they will shuttle you north or south to start your hike and will pick you up at the end and bring you back to your car. (I compared their prices with 3 other services and all were within $10+-). I will use their service again this year and highly recommend them.
Enjoy your hike!