For reference:
https://www.nps.gov/grsm/planyourvis...omplete4-2.pdf
Here is an option for doing the GSMNP northbound and staying at backcountry campsites where you can legally use your hammock. It adds a bunch of extra miles and all campsites are downhill from the AT so lots of extra ups and downs.
Day 1 - Fontana to 113 - 4.4mi +3100ft -1300ft
Day 2 - 113 to 9 - 13.1mi +4300ft -4800ft
Day 3 - 9 to 26 - 13.4mi +6100ft -4900ft
Day 4 - 26 to 46 - 13.5mi +4600ft -5300ft
Day 5 - 46 to Newfound Gap - 10.2mi +3800ft -2600ft
Spend night in Gatlinburg and resupply... or come back another time
Day 6 - Newfound Gap to 49 - 9.0mi +2600ft - 4500ft
Day 7 - 49 to 29 - 21.5mi +9000ft -7500ft
Day 8 - 29 to 37 - 9.2mi +2700ft -4300ft
Day 9 - 37 to Davenport Gap - 9.2mi +3200ft -4200ft
Totals for this nontraditional hike: 103.5mi +39,400ft -39,400ft
Total for traditional hike staying at shelters: 72mi +26,600ft -26500ft
Data taken from National Geographic Topo! (defunct software)