2x2x2/2x2x3 Blockbuilding?

[Hazel]

I'm a CFOP solver, but I enjoy making example solves of Hexagonal Francisco. In the spoiler I have a list of example solves I've made, and based on those what specific tips for making more efficient 2x2x2/2x2x3 blocks would you have?
For clarification, the steps I'm doing are:
1) 2x2x2
2) Expand to 2x2x3
3) solve an F2L corner-edge pair plus the other E-layer edge
4) Solve last D-layer edge while solving EO
5) CLS
6) PLL

Spoiler

1) L D2 L' D2 R' B2 D2 B2 L D2 U' L2 B' L F' D2 F2 U L2 B2

x' D' R' D R2 x' // 2x2x2
U' L F L2 U2 S U' S' // 2x2x3
L F L' U' F2 U2 F // CE+E
U' M' U M U2 M' U2 M // EODF
U' R U' R' U' R U R' U2 R U' R' // CLS
U x U2 r' U' r U2 l' U R' U' R2 // J Perm

56 HTM, 50 STM

2) R' F B2 D' R2 D' F' R' U' B U2 F R2 U2 R2 F' R2 B' R2 F2

x2 L' U' R' F R U' R' // 2x2x2
U' L B L' d' L U L' // 2x2x3
R' U R2 U' R2 y R' F R // CE+E
U M' U M U2 M' U2 M // EOFF
y' R U' R2 U' R U' R' U2 R2 U R' // CLS
R2 U R U R' U' R' U' R' U R' U2 // Ub Perm

58 HTM, 54 STM

3) B2 L F2 B U' R' L2 F R D2 R2 D2 L' F2 U2 D2 L B2 L'

z2 U' D' B2 L' U L' R' F L2 // 2x2x2
R B2 d B2 U R' U2 R // 2x2x3
U L U2 L' U L' d // CE+E
M' U M U2 M' U' M // EODF
U2 R U R' U' R U R' U R U' R' // CLS
U2 R U R' F' R U R' U' R' F R2 U' R' U2 // J Perm

52 HTM, 58 STM

4) L2 R2 F2 U R2 D R2 F2 U2 R2 U' L' F2 D' B L' D L2 F D B

F D' B' R' L U' L' F U' R' D2 // 2x2x2
L' U' L U2 B' U' L' U F U F' // 2x2x3
y U R2 U' R' U R // CE+E
y U M' U M U2 M' U2 M // EODF
R U' R' U' R U' R' U2 R U R' // CLS
U2 R' U2 R U2 R' F R U R' U' R' F' R2 // Rb Perm

5) R2 U' L2 B2 F2 U' F2 U B2 D' B' U' L2 F2 R U' F' D2 U2 L

z2 F' U' R' D d R' U' R // 2x2x3
F' U' F L' U L r U r' // CE+E
U M' U' M // EODF
R U' R' U2 R U' R U2 R2 U' R2 U' R2 // CLS
R' U L' U2 R U' M' B r' U2 R U' L U' // Nb Perm

51 HTM, 48 STM

6) F2 U2 R' D R' B' D' F D' F2 U2 L U2 D2 F2 R' F2 R L D2

L' D' B D2 L' B' L // 2x2x2
M' U2 M U R2 U2 F' R // 2x2x3
L' U' L F' U' F // CE+E
U2 M' U2 M // EODF
y' R' U' R U2 R' U2 R U2 R' U' R // CLS
U2 F R U' R' U' R U R' F' R U R' U' R' F R F' U // Y Perm

59 HTM, 55 STM

7) U2 L2 B2 D2 F' L2 F R2 B R2 F L F2 U2 F' D L' R' B U' R'

L2 F' U' R' L B' U' R' U' B U2 B' // 2x2x2
y' U' M' U2 M U R' U2 R // 2x2x3
U F U F' // CE+E
U' M' U' M U2 M' U M U M' U2 M // EODF
y' R' U' R U' R' U' R U R' U2 R // CLS
M2 U' M U2 M' U' M2 U2 // Ub Perm

67 HTM, 55 STM

 

[xyzzy]

My solutions for the 2×2×2 blocks:
1: x' y F2 R2 U F'
2: x' y M U L2 D' F'
3: x2 R2 D' R D B' R'
4: z2 U' R' F' L D2 F'
5: x y2 R' U R U2 R'
6: x2 y' R2 B R2 U' R U2
7: x' R2 U2 R2 U' R' U' or z2 D R' F D L

Not all of them are better than yours (e.g. obviously your 8-move 2×2×3 for #5 is better than my 5-move 2×2×2), but they certainly are shorter on average. You should be aiming for 6-7 moves for the block (8+ is acceptable if that lets you plan ahead further, of course).

Some of your longer solutions look sort of like you're trying to solve a partial cross, then insert the corner and edge separately keyhole-style. This works sometimes, but I find that it's more useful when solving more than just a 2×2×2 (e.g. xcross or 2×2×3).