I figured out a neat method for this puzzle. It's like ZZ in that orientation is done first and then permutation. I attached a pdf guide. I solved the two examples in the guide in 27 and 31 moves if I remember correctly so I'm sure it could be done shorter and faster with some practice and...

Hey those aren't all 2-gen...
R U R U R2 U (U R U R U' R' U' R' U' R) R U' R2 U'
pseudo-f2l, inserted alg cycles 3 edges
vlew
Next: U' M2 U M2 U2 M U2 M2 U M U2 M2 U M2 U2 M' U' M' U2 M' U M2 U M2 U'

U R' U2 R2 U' R' U' R' U //pseudo-f2l
R U2 R' U' R U R' U' R U' R' //double antisune
R //fix
view
Next: U2 M U' M U2 M' U' M U' M' U' M2 U' M U2 M2 U M2 U2 M U2 M2 U M2 U2

U2 R U2 R' U2 R2 U' R' U' R U2 R' U2 R //f2l
R' U2 R2 U2 R2 U' R2 U' R2 U R U //benny
view
Next: U' R U' R2 U2 R' U2 R' U2 R2 U2 R2 U R' U2 R' U2 R' U' R U' R' U R2 U2

Filipe's scramble: U2 R U' R2 U' R' U2 R U2 R' U' R2 U R' U2 R' U2 R U R' U2 R2 U R' U2
U2//random turn, legit fmc technique
R' U' R' U2 R2 U R2 U' R2 U R //f2l
U' R2 U R U' R U R2 // antisune
view
R2 U R' U2 R2 U R2 U' R U R //pseudo f2l
U' R' U R' U' R2 U // sune
U2 //fix
view
Next: U2 M'...

F' L F' L' F2 U'
[U2 F': U2 F' U2 F2 U F2 U F2 U2 F'] //bruno
= F' L F' L' F2 U F' U2 F' U2 F2 U F2 U F2
edit: oh no, I just found the inverse of scramble
F' // pseudo-f2l
U F B2 R' B R' B' R2 B R' B F' //oll
F U //fix pseudo, leaves 3 corners
[U, R' D' R]
= F' U F B2 R' B R' B' R2 B R' B U2...

R2 U2 R' U2 R2 U (U'R'U' RURUR U'R') R' U' R' U' R' U2 R U2 R2
insertion cycles 3 edges
= R2 U2 R' U2 R U' R U R U R U' R2 U' R' U' R' U2 R U2 R2
Next: M U' M U' M2 U M2 U' M' U2 M U2 M U' M U M U2 M' U' M2 U' M U M'

F U2 F2 U' F2 U' F'
R' U' F' U F R
R' U' R U' R' U2 R
(not a speed solve, i almost always use oll then pll)
view
F' U L' U2 L U2 F is nice, gets into 2genLL but then I don't know this case in one alg
Next: R U R' L' B' R B' D2 F2 R B2 L B2 R2 D2 B2 U2

found using the inverse of scramble:
(U' R U' R' U' R' U' //pseudo-f2l, premove R'
R U2 R' U' R U' R') //antisune
= R2 U R' U R U2' R' U R U R U R' U
Next: L U2 L' U L' U L2 U' L' U L' U L U L' U' L2 U2 L U2 L2 U L U2 L

R' U2 R U' R' U' R' U' R2 U R' U2 (U'R'U'R'U' RURUR) R U' R'
insertion to cycle 3 edges
= R' U2 R U' R' U' R' U' R2 U R' U R' U' R' U' R U R U R2 U' R'
Next: M U' M2 U2 M U M U2 M2 U' M' U2 M U' M' U2 M' U2 M U' M' U M' U' M'

Guys, don't get hung up over the title whether it's really actually impossible or almost impossible or nearly impossible or just difficult but possible... Anyway, if you're not familiar with the series, it's something like "Even against physical and physiological limits, humans are capable of...

scramble from cstimer: U2 R2 U R2 U' F2 D R2 D
solution 1: ortega method
U b2 D' r2 \\separate
U r2 U' b2 U2 r2 D' f2 //pbl
U'
view (using the 4x4x4 sim)
solution 2:
U' r2 e U r2 //D
y2 r2 U' r2 U r2 y r2 U r2 3Uw' r2 //domino T-perm
D' U'
view
Next: R2 U R2 U' F2 D R2 U R2

F2 U2 F2 D2 B2 D2 // alternative to U2B2U2B2U2, maybe more opportunities for insertions but i didn't check
F2 U2 (U2F2U2R2 U2F2U2R2) F2 D2 B2 D2 //insertion to cycle 3 edges
= U2 R2 U2 F2 U2 R2 F2 D2 B2 D2 // cancels 4 moves
U2 R2(R2U2L2 B2 L2U2R2 F2) U2 F2 U2 R2 F2 D2 B2 D2 // cycle another 3...