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Red bordered cages are consecutive, fully ordered (CFO)

Prelims (the CFO cages on D\ are covered by step 1)
a) CFO cage at R1C9: no 8,9 in R1C9, no 1,9 in R2C8, no 1,2 in R3C7
b) CFO cage at R4C5: no 9 in R4C5, no 1 in R4C6
c) CFO cage at R4C8: no 9 in R4C8, no 1 in R5C9
d) CFO cage at R5C3: no 9 in R5C2, no 1 in R5C3
e) CFO cage at R5C7: no 9 in R5C7, no 1 in R5C8
f) CFO cage at R6C5: no 9 in R6C4, no 1 in R6C5
g) CFO cage at R7C3: no 8,9 in R7C3, no 1,9 in R8C2, no 1,2 in R9C1

1. The three CFO cages on D\ must be [123/456/789] -> R1C1 + R4C4 + R7C7 = {147}, R2C2 + R5C5 + R8C8 = {258}, R3C3 + R6C6 + R9C9 = {369}
1a. R2C2 + R5C5 + R8C8 = {258}, CPE no 2,5,8 in R2C8 + R8C2 using D/ R1C9
1b. R2C8 = {3467} -> CFO cage at R1C9 = [234/345/567/678], no 1,4,7 in R1C9, no 3,6,9 in R3C7
1c. R8C2 = {3467} -> CFO cage at R7C3 = [234/345/567/678], no 1,4,7 in R7C3, no 3,6,9 in R9C1

2. R6C4 = 1, R4C6 = 9 (hidden singles on D/), R4C5 = 8, placed for D\ R1C2 and D/ R1C8, R6C5 = 2, placed for D\ R2C1 and D/ R2C9
2a. R5C5 = 5, placed for both long diagonals -> R4C4 = 4, R6C6 = 6, both placed for D\
2b. Naked pair {37} in R5C46, locked for R5
2c. Naked pair {17} in R1C1 + R7C7, CPE no 1,7 in R1C7 + R7C1
2d. Naked pair {39} in R3C3 + R9C9, CPE no 3,9 in R3C9 + R9C3
[First time through, I overlooked the important step 2e until much later; I’ve re-worked with it in the right place, removing a heavy step after all the cages had been placed.]
2e. Naked pair {37} in R5C46, CPE no 3,7 in R3C4 using D\ R1C2, no 3,7 in R7C6 using D\ R2C1

3. The two CFO cages on D/ must be [234/678] -> R1C9 + R7C3 = {26}, R2C8 + R8C2 = {37}, R3C7 + R9C1 = {48}
3a. Naked pair {26} in R1C9 + R7C3, CPE no 2,6 in R1C3 + R7C9
3b. Naked pair {48} in R3C7 + R9C1, CPE no 4,8 in R3C1 + R9C7

4. R5C23 = [12/89], R5C78 = [12/89], naked quad {1289} in R5C2378, locked for R5
4a. CFO cage at R4C8 = [34/56], R4C8 = {35}, R5C9 = {46}

5. CFO cage at R1C1 = [123] or CFO cage = [789] => R5C23 = [12], CPE no 1 in R13C2 + R4C1, no 2 in R2C3 + R4C2

6. CFO cage at R1C9 = [234] => CFO cage at R4C8 = [56] or CFO cage at R1C9 = [678]
-> 6 in R15C9, locked for C9

7. CFO cage at R7C3 = [234] or CFO cage at R1C9 = [234] => CFO cage at R4C8 = [56] => R5C1 = 4
-> 4 in R59C1, locked for C1

8. CFO cage at R4C8 = [34] or CFO cage at R4C8 = [56] => CFO cage at R1C9 = [234]
-> 3 in R24C8, locked for C8
and 4 in R3C7 + R5C9, CPE no 4 in R23C9 + R6C7

9. CFO cage at R5C2 = [12] => CFO cage at R7C3 = [678] or CFO cage at R5C2 = [89]
-> 8 in R5C2 + R9C1, CPE no 8 in R6C1 + R9C2

10. CFO cage at R5C7 = [12] => CFO cage at R7C7 = [789] or CFO cage at R5C7 = [89]
-> 8 in R5C7 + R8C8, CPE no 8 in R6C8 + R8C7
and 9 in R5C8 and R9C9, CPE no 9 in R6C9 + R79C8

11. CFO cage at R5C2 = [12] => CFO cage at R7C3 = [678] or CFO cage at R5C7 = [12] => CFO cage at R7C7 = [789]
-> 7 in R7C7 + R8C2, CPE no 7 in R7C2 + R8C79
and 8 in R8C8 + R9C1, CPE no 8 in R8C3 and R9C8

12. CFO cage at R5C7 = [12] or CFO cage at R5C7 = [89] => CFO cage at R1C9 = [234] -> 2 in R1C9 + R5C8, CPE no 2 in R1C8 + R4C9

13. R5C8 = 2 (hidden single in N6), R5C7 = 1, R5C23 = [89], CFO cage at R1C1 = [123], CFO cage at R7C7 = [789]

14. R4C1 = 2 (hidden single in R4), R6C9 = 8 (hidden single in R6)

15. CFO cage at R4C8 = [34] or CFO cage at R4C8 = [56] => R4C7 = 3
-> 3 in R4C78, locked for R4 and N6

16. CFO cage at R7C3 = [678] or CFO cage at R7C3 = [234] => R5C1 = 6 -> 6 in R5C1 + R7C3, CPE no 6 in R4C3 + R78C1

17. CFO cage at R4C8 = [34] => R2C8 = 7 or CFO cage at R4C8 = [56] => R4C9 = 7
-> 7 in R2C8 + R4C9, CPE no 7 in R23C9 + R6C8

18. R4C9 = 7 (hidden single in N6)

[Just spotted …]
19. R7C3 = 2 (hidden single in R7) -> CFO cage at R7C3 = [234], CFO cage at R1C9 = [678], R5C19 = [64], R4C8 = 3

20. Naked pair {15} in R4C23, locked for R4 and N4 -> R4C7 = 6, placed for D/ R2C9
20a. R6C1 = 3 (hidden single in N4)
20b. Naked pair {59} in R6C78, CPE no 5 in R7C8 using D\ R1C2

21. 6 in R8 only in R8C45, locked for N8
21a. 6 in R2 only in R2C3456, CPE no 6 in R3C4 using D\ R1C2

22. 7 in C1 only in R38C1, CPE no 7 in R3C6 using D/ R1C8
22a. 8 in C1 only in R27C1, CPE no 8 in R7C6 using D\ R2C1
22b. 2 in C9 only in R38C1, CPE no 2 in R3C4 using D\ R1C2
22c. 3 in C9 only in R27C9, CPE no 3 in R7C4 using D/ R2C9

23. Naked pair {59} in R3C4 and R6C7, locked for D\ R1C2

24. Naked quad {1357} in R2C9 + R6C5 + R8C3 + R9C2, locked for D/ R2C9

25. R79C8 = {16} (hidden pair in C8), locked for N9 -> R8C9 = 2
25a. R8C7 = 4 (hidden single in N9), placed for D\ R2C1
25b. R7C5 = 4 (hidden single in N8)

26. Naked pair {15} in R4C3 and R7C6, locked for D\ R2C1 -> R9C8 = 6, placed for D\ R2C1, R7C8 = 1, R7C9 = 3, R9C7 = 5, R6C7 = 9, placed for D\ R1C2, R3C4 = 5
26a. Naked pair {79} in R3C2, locked for R3 and N1 -> R3C89 = [41], R2C9 = 5, placed for D/ R2C9

27. Naked pair {17} in R8C3 + R9C2, locked for D/ R2C9 and N7 -> R5C6 = 3

and the rest is naked singles, without using the diagonals.

I'll rate my walkthrough for Consecutive, Fully Ordered, Triple Diagonal 7 at 1.5. While each of my short forcing chains are Easy 1.5 steps, I used so many of them that I've got to go for the full 1.5. I used them in the order I spotted them until I found a useful hidden single; then I used some more until I found another useful hidden single.