Hey Dennis,
First off, I love your site and I use it a lot. I think my differences may just be stylistic. It took me a while to understand that Dan Knights' cases were in [R,U], so until then I was always questioning why he'd use a 12 move alg when a 9 move existed. Obviously the 9 move was not in [R,U].
I have to head to work, but just in the first set of adjacent slot examples, in the second case, you have a seven move alg with two double turns on three faces: L' U2 R U2 L U' R', I'd solve it with U R U R' U' R U R', eight moves, but fast, fast. In the third case you solve with, L U' R U L' U2 R' (8 moves), I'd choose U R U' R' U R U' R', still eight moves, but all in [R,U], but it doesn't use the empty slot, which is the purpose of the list.
They're really just stylistic differences and entirely personal preference, I've never actually found any that were wrong. The cases, as solved, are useful for playing with alternative insertions and learning to use the empty slots, but as with everything, you have to pick the algs that suit your style.
Hope you didn't take it as a criticism, I use your site a lot.