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Next: B2 U' D2 L2 R2 F2 U2 F' L2 F U2 R2 U' F' L' D2 U' B' D' R2

// CP-Roux?
y' // CP case: 32, #2 in position X swaps with #4
U2 R' F // CP line (3)
R u' R' u E' R u' // pEO extension (7/10)
r U2 r U2 r U' r' U' r' U2 r // EOBF + dBR (11/21)
S' U2 S U2 R U' R' U R U R' // F2B (11/32)
U R U2 R2 U' R2 U' R2 U2 R // OCLL (10/42)
U M2 U' M' U2 M' U2 M2 // M2+4c (8/50)
U' // AUF (1/51)

NEXT: R2 U B L F2 D2 L U2 L' D2 U2 R D2 R' B U' B' F R' D B2

x2 y // CP case: 23
U' F' U' f U' S' // CP line (6)
u2 R' U R' u' R E R2 U R // belt (10/16)
M U' r2 U2 M // EOdM (5/21)
U' R2 U R U R U2 R' U R // F2L (10/31)
R U2 R' U' R U' R' // OCLL (7/38)
U2 S U2 S U' S' U2 S' U2 // L5EP (9/47)

NEXT: D' F2 R2 F2 D L2 R2 B2 D F2 L' F2 U' R2 B' U' L D' U' R'

x2 y2
S' R2 U R' F2 // CP line (5)
U' u' r M' U r2 // Mehta CPFB (6/11)
u' R u R U' R' // 3QB (6/17)
u U R' U R U' R' U' R // pLS (9/26)
M U R U R' U' M2 U R U' r' // EO (11/37)
U' R U R' U R U2 R' U2 R U2 R' U' R U' R' // 2GLL (16/53)
u2 U' // AUF (2/55)

NEXT:
D2 F2 U2 L2 U2 F' R2 B D2 B2 L' F R U2 L2 F2 U B F'

I made a video with 5 example solves. pEO-ext is definitely not the most efficient, but I've been trying out the method for a little amount of time yet so any better solution suggestion would be much appreciated

x2 y2
S' R2 U R' F2 // CP line (5)
U' u' r M' U r2 // Mehta CPFB (6/11)
u' R u R U' R' // 3QB (6/17)
u U R' U R U' R' U' R // pLS (9/26)
M U R U R' U' M2 U R U' r' // EO (11/37)
U' R U R' U R U2 R' U2 R U2 R' U' R U' R' // 2GLL (16/53)
u2 U' // AUF (2/55)

NEXT:
D2 F2 U2 L2 U2 F' R2 B D2 B2 L' F R U2 L2 F2 U B F'

y // using my own simplified YruRU CP recognition
// after S2 F':
// corners case: 13: R5413
// swap case: U312: (F' U F)
f2 U F r' // CP line (4)
E u' R' u R' E2 r U' R2 U' r // belt (11/15)
M U' M' r2 U2 M U2 M // EOdM+DFR (8/23)
U R' U R S' U2 S R' U R // mirrored TDR-2 (10/33)
U2 R U2 R' U' R U' R' // 2GLL (8/41)
U' // AUF (1/42)

NEXT:
D' U2 B U2 F L2 B R2 B2 L2 D2 B L' D B' U B2 R2 B2 U2

My video doesn't actually go through exactly how 2GR CP works. It goes through the underlying theory of both 2GR and YruRU style. Here's the website though: https://john-ml.github.io/2GR/CPLine/CPLine.html

y z
// visualize R
// tracelet: 5-6-3-4-1-2
// CP case: 13 [R54132]
// corner in pos. #X is #6
// #6 must swap with #1
R' U' R // so #1 must be in pos. #3
F2 u S2 M // CP line + DFM (7)
U' M U' M' // dM (4/11)
R E R E R' U' R' u' // 3QB (8/19)
S' U S U R U' R' // EOLE (7/26)
U R2 U' R2 U' R2 U2 R2 // DBR (8/34)
U R U' R' U2 R U R' U R' U' R U R U R' U' R' U R // 2GLL (20/54)
E2 // AEF (1/55)

NEXT:
F' U' F2 R' D B L' U B2 U2 L B2 R' F2 L' D2 L D2 F2 L U'