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The same number is missing from each of the 8-cell diagonals

Prelims

a) R1C34 = {17/26/35}, no 4,8,9
b) R1C67 = {17/26/35}, no 4,8,9
c) R34C1 = {19/28/37/46}, no 5
d) R34C9 = {13}
e) R67C1 = {18/27/36/45}, no 9
f) R67C9 = {17/26/35}, no 4,8,9
g) R9C34 = {15/24}
h) R9C67 = {13}
i) 22(3) cage at R1C1 = {589/679}
j) 20(3) cage at R5C7 = {389/479/569/578}, no 1,2
k) 30(4) disjoint cage at R1C8 = {6789}
l) 37(6) disjoint cage at R2C1 = {256789/346789}, no 1

Steps resulting from Prelims
1a. Naked pair {13} in R34C9, locked for C9, clean-up: no 5,7 in R67C9
1b. Naked pair {26} in R67C9, locked for C9
1c. Naked pair {13} in R9C67, locked for R9, clean-up: no 5 in R9C34
1d. Naked pair {24} in R9C34, locked for R9
1e. 22(3) cage at R1C1 = {589/679}, 9 locked for C5 and N2

2. 45 rule on C5 3 innies R456C5 = 8 = {125/134}, 1 locked for C5 and N5

3. 45 rule on R5 3 innies R5C456 = 11 = {128/137/146/236/245}, no 9

[It looks like thought now needs to be given to the 8-cell diagonals which each have the same total.]
4. 8-cell diagonals must contain all of 6,7,8,9 (because of 30(4) disjoint cage at R1C8) -> missing number on these diagonals must be one of 1,2,3,4,5

[I don’t usually re-work except when I’ve made mistakes or missed obvious moves, but this step belongs here. It feels a bit more like a Paper Solvable step than normal elimination solving.]
5. 37(6) cage at R2C1 -> R5C4 + R6C5 + missing number on 8-cell diagonal at R2C1 form hidden 8(3) cage = {125/134} -> R6C5 = 1 (R5C4 + R6C5 cannot be {25/34} which clash with hidden 8(3) cage R456C5, CCC), clean-up: no 8 in R7C1

6. 30(7) cage at R2C7 contains all of 1,2,3,4,5, they cannot all be on 8-cell diagonal -> R4C4 = {2345}
6a. The number in R4C4 will be the one missing from the 8-cell diagonals

7. 30(4) disjoint cage at R1C8 + 30(7) cage at R2C7 + 32(7) cage at R3C8 contain both 8-cell / diagonals plus two outies R4C4 + R6C6
7a. 30(4) disjoint cage at R1C8 + 30(7) cage at R2C7 + 32(7) cage at R3C8 = 92, total of two 8-cell diagonals is even -> R4C4 + R6C6 must be even
7b. Min R4C4 + R6C6 = 8 (cannot be 4 or 6 because no 1 in R4C4 + R6C6 and {24} clashes with R456C5) -> max for two 8-cell diagonals = 84 -> total on 8-cell diagonals = 40,41,42 (cannot be lower because they contain all of 6,7,8,9), missing number on these diagonals is one of 3,4,5 -> R4C4 = {345} (step 6a)
7c. R4C4 + R6C6 = 8,10,12 = [37/46/39/48/57] (cannot be {35} which clashes with R456C5) -> R6C6 = {6789}
7d. R4C4 + R6C6 = 10,12 -> max for two 8-cell diagonals = 82 -> total for 8-cell diagonals = 40,41 -> missing number on these diagonals is one of 4,5 -> R4C4 = {45} (step 6a)
7e. R4C4 + R6C6 = [46/48/57] -> R6C6 = {678}

8. Max 8-cell diagonals = 41 -> max R5C4 = 3
8a. Naked quad {2345} in R45C45, locked for N5

9. R5C456 (step 3) = {236} (only remaining combination) -> R5C6 = 6, placed for 8-cell diagonals at R1C2 and R2C9, R5C45 = {23}, locked for R5 and N5, clean-up: no 2 in R1C7
9a. Naked pair {45} in R4C45, locked for R4 and 30(7) cage at R2C7, no 4,5 in R2C7 + R3C8 + R6C3 + R7C2, clean-up: no 6 in R3C1

10. 1 in R5 only in 14(3) cage at R5C1, locked for N4, clean-up: no 9 in R3C1
10a. 14(3) cage = {149/158}, no 7
10b. 7 in R5 only in 20(3) cage at R5C7, locked for N6

11. R4C4 + R6C6 (step 7e) = [48/57] = 12 -> total for two 8-cell diagonals = 80 (step 7a) -> total for each 8-cell diagonal = 40 -> no 5 on 8-cells diagonals -> R4C5 = 4, placed for 8-cell diagonal at R1C2, R5C5 = 3 (step 2), R4C4 = 5, R5C4 = 2, placed for 8-cell diagonal at R2C1, R6C6 = 7, R9C34 = [24], clean-up: no 3,6 in R1C3, no 6 in R1C4, no 1 in R1C7
11a. 2 in C5 only in 15(3) cage at R7C5, locked for N8

12. 30(4) disjoint cage at R1C8 = {6789}, 6 locked for 8-cell diagonal at R1C8

13. 30(7) cage at R2C7 = {1234578} (only remaining combination), no 9, 7,8 locked for 8-cell diagonal at R1C8, CPE no 7 in R7C7
13a. Naked pair {69} in R1C8 + R8C1, locked for 30(4) disjoint cage at R1C8 -> R2C9 + R9C2 = {78}, locked for 8-cell diagonal at R2C9
13b. Naked pair {69} in R1C8 + R8C1, CPE no 6,9 in R1C1 + R8C8
13c. Naked pair {78} in R2C9 + R9C2, CPE no 7,8 in R2C2 + R9C9

14. 32(7) cage at R3C8 = {1234679}, CPE no 2 in R3C7 + R4C8, no 4 in R3C3 + R8C8
14a. 2 in N3 only in R23C8, locked for C8
14b. R8C5 = 2 (hidden single in R8)

15. 30(6) disjoint cage at R1C2 = {123789}, CPE no 2 in R6C2

16. R2C6 = 4 (hidden single in C6)

17. 37(6) cage at R2C1 = {346789}, CPE no 4 in R3C7 + R8C2

18. Caged X-Wing for 4 in 37(6) disjoint cage at R2C1 and 32(7) cage at R3C8, no other 4 in R3, clean-up: no 6 in R4C1

[Only just spotted …, although only a couple of steps late]
19. R1C6 = 2 (hidden single in C6), R1C7 = 6, R1C8 = 9, R8C1 = 6, clean-up: no 3 in R67C1

20. 6 in N8 only in 15(3) cage at R7C5 = {267} (only remaining combination), locked for C5 and N8

21. Naked triple {589} in 22(3) cage at R1C5, locked for N2
21a. Naked pair {13} in R39C6, locked for C6
21b. R8C6 = 5 (hidden single in C6)
21c. R2C4 = 6 (hidden single in N2)

22. 30(6) disjoint cage at R1C2 = {123789} -> R6C7 = 2, R67C9 = [62], clean-up: no 7 in R7C1

23. 32(7) cage at R3C8 = {1234679} -> R3C8 = 2, clean-up: no 8 in R4C1

24. R4C1 = 2 (hidden single in C1), R3C1 = 8, clean-up: no 1 in R7C1
24a. Naked pair {45} in R67C1, locked for C1
24b. R9C9 = 5 (hidden single in R9)

25. 30(6) disjoint cage at R1C2 = {123789}, 8 locked for N9

26. 3 in C1 only in R12C1, locked for N1

27. 30(6) disjoint cage at R1C2 = {123789}, CPE no 3 in R7C4 -> R7C4 = 9

and the rest is naked singles.

My solving path could have been shorter if I'd found hidden singles and CPEs in a better order.

I'll rate my walkthrough for Double Diagonal 4 at least 1.25. My first breakthrough step used CCC between a hidden 3-cell cage and a hidden virtual 3-cell cage.

Note that there is no SS score for this puzzle because the code string only generates the basic cage pattern without the 8-cell diagonals.