Thanks for the tips. I took a shot at mapping it using your suggestion for Icewater Spring Shelter for Night 2. I still want to get over to Charlies Bunion so I added that as an out and back along the AT once I get to Icewater Springs. The route is otherwise as I described above. It totals 40 miles over 4 days, with the last day being the longest at ~14.5 miles. The link to the Caltopo map is below.
https://caltopo.com/m/GKLLT
Day 1: 5.1 miles up Alum Cave Trail to Mt LeConte Shelter
Day 2: 6.7 miles down Boulevard Trail to Icewater Springs and then another 6.7 miles out and back to Charlies Buinion (13.3 miles total)
Day 3: 7.7 miles along AT from Icewater Springs to Mt Collins Shelter
Day 4: 3.4 miles from Mt Collins Shelter to Clingmans Dome and then 11 miles back along AT to Prong Trail to Chimney Tops Trail and back to Rte 441.
To anyone thinking about joining, I need to book permits this Wednesday night in order to secure weekend reservations in April. Feel free to PM or post here if you would like to join.