I used to live near LBL since 1989 and have explored almost every backroad and trail in the place, more in the KY portion, a little less in TN. Glad you found it to your liking. A few observations: there are few boondock sites that someone doesn't think is their own and a few can be downright rude about moving in next to you and making you feel unwelcome. It's a redneck thing. Usually loud music and drunkenness too. And trash as you have seen. They come by boat or truck so no place is too remote. Summer holidays are very crowded. I have found that the Barkley side can be a little less visited because the bays are usually shallower/muddier but that means poorer swimming. I usually carried a canoe or kayak so I could paddle to better swimming spots. Fishing is usually very good in those bays. Be careful getting too far off roads as you can be ticketed for leaving numbered roads. Speaking of numbered roads there is a number system that denotes amount of maintenance used. Roads numbered in 100s are usually paved or smooth gravel and range to 400s which are very primitive. There are not many of the latter. You have spoken with the rangers, probably Bill and Kyle, so much of this is not new to you. One last caution: LBL is famous for its ticks. The spray that is sold in the visitor centers works best.
My favorite time of year in LBL is the fall, late Sept to about mid-Nov. Fall colors are brilliant, day temps are comfortable, nights are cool for sleeping, lakes are low exposing more beaches and after the first frost ticks are much fewer.
I now live in Colorado but know I will miss LBL, especially come fall. I hope you and your family will enjoy "my backyard" for years to come.
Ace