Since the 17(5) cage in the Assassin was mostly effective toward the end of my solving path, I’ve used as much of that as possible. The first major difference is at the end of step 6, when a hidden single in N2 is no longer available, while much of the original step 7 is still valid.
Prelims
a) 7(2) cage at R1C2 = {16/25/34}, no 7,8,9
b) 13(2) cage at R1C8 = {49/58/67}, no 1,2,3
c) 13(2) cage at R8C1 = {49/58/67}, no 1,2,3
d) 7(2) cage at R8C9 = {16/25/34}, no 7,8,9
e) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
f) 10(3) cage at R6C5 = {127/136/145/235}, no 8,9
g) 23(3) cage at R6C7 = {689}
h) 10(3) cage at R7C5 = {127/136/145/235}, no 8,9
1. 23(3) cage at R6C7 = {689}, CPE no 6,8,9 in R789C7
2. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on D/ 3 innies R4C6 + R5C5 + R6C4 = 9 = {126/135/234}, no 7,8,9
2b. R5C5 = {456} -> no 4,5,6 in R46C46
3. 45 rule on N1 2(1+1) outies R1C4 + R4C1 = 11 = {29/38/47/56}, no 1
4. 45 rule on N9 2(1+1) outies R6C7 + R9C6 = 14 = [68/86/95]
4a. 17(3) cage at R8C7 = {278/458/467} (cannot be {368} because 6,8 only in R9C6), no 1,3
4b. 6,8 only in R9C6 -> R9C6 = {68} -> R6C7 = {68}
4c. Naked pair {68} in R6C7 + R9C6, CPE no 8 in R6C6
4d. 23(3) cage at R6C7 = {689}, 9 locked for R7 and N9
5. 45 rule on N3 4 innies R12C7 + R3C89 = 14 = {1238/1247/1256/1346/2345}, no 9
6. 12(3) cage at R1C1 = {129/138/147/156/237/345} (cannot be {246} which clashes with 7(2) cage at R1C2)
6a. 17(3) cage at R8C7 (step 4a) = {278/458/467} -> R89C7 = {27/45/47}
6b. 12(3) cage at R7C7 = {156/237/345} (cannot be {138} which clashes with 12(3) cage at R1C1, cannot be {147/246} which clash with R89C7), no 8
6c. 8 in N9 only in R7C89, locked for R7 and 23(3) cage at R6C7 -> R6C7 = 6, R9C6 = 8 (step 4) -> R89C7 = {27/45}, clean-up: no 5 in R8C1
6d. Killer pair 5,7 in 12(3) cage at R7C7 and R89C7, locked for N9, clean-up: no 2 in 7(2) cage at R8C9
6e. 12(3) cage at R1C1 = {129/156/237} (cannot be {138/147/345} which clash with 12(3) cage at R7C7, no 4,8
6f. 7(2) cage at R1C2 = {16/34} (cannot be {25} which clashes with 12(3) cage at R1C1)
6g. Killer pair 1,3 in 12(3) cage at R1C1 and 7(2) cage at R1C2, locked for N1
6h. R4C4 = 8 (hidden single in D\) -> R5C5 + R6C6 = 13 (step 2) = [49/67], clean-up: no 3 in R1C4 + R4C1 (step 3)
6i. R4C6 + R5C5 + R6C4 (step 2a) = {126/234}, 2 locked for N5 and D/
7. 18(3) cage at R1C9 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7a. 18(3) cage at R7C3 = {189/378/459/567} (cannot be {468} which clashes with R5C5, cannot be {369} which clashes with R4C6 + R5C5 + R6C4)
7b. 13(2) cage at R1C8 = {49/67} (cannot be {58} which clashes with 18(3) cage at R1C9), no 5,8
7c. 13(2) cage at R8C1 = {49/67} (cannot be [85] which clashes with 18(3) cage at R7C3), no 5,8
7d. R8C2 = 8 (hidden single in N7), placed for D/ -> 18(3) cage at R7C3 = {189/378}, no 4,5,6, no 1 in R9C1
7e. Killer pair 7,9 in 18(3) cage at R7C3 and 13(2) cage at R8C1, locked for N7
7f. Killer pair 1,3 in R4C6 + R6C4 and 18(3) cage at R7C3, locked for D/
7g. Naked quint {45679} in 13(2) cage at R1C8 + 18(3) cage, locked for N3
8. 18(3) cage at R1C7 = {189/279/369/378/468} (cannot be {459/567} because R1C7 only contains 1,2,3,8), no 5
8a. 2 of {279} must be in R1C7 -> no 2 in R2C6 + R3C5
8b. 18(3) cage at R2C7 = {189/369/378/468} (cannot be {459/567} because R2C7 only contains 1,2,3,8, cannot be {279} because 2{79} clashes with R6C6), no 2,5
8c. 8 of {189} must be in R2C7 -> no 1 in R2C7
8d. 18(3) cage at R5C3 = {189/279/369/378/459/468/567}
8e. 1,2 of {189/279} must be in R7C1 -> no 1,2 in R5C3 + R6C2
8f. 18(3) cage at R5C4 = {189/369/378/459/468/567} (cannot be {279} because {79}2 clashes with R6C6), no 2
8g. 1 of {189} must be in R7C2 -> no 1 in R5C4 + R6C3
8h. 1 in N3 only in R1C7 + R3C89, CPE no 1 in R3C5
[It looks like it’s time to start using forcing chains.]
9. 8 in N1 only in R12C3 + R3C1
9a Consider permutations for R1C4 + R4C1 (step 3) = {29/47/56}
R1C4 = 2 -> R12C3 = 17 = {89}
or R1C4 = 4 => R4C1 = 7 => R3C12 = 11 = {29/56} => R12C3 = 15 = {78}
or R1C4 = 5 => R12C3 = 14 = {68}
or R1C4 = 6 => R4C1 = 5 => R3C12 = 13 = {49/67} => R12C3 = 13 = {58}
or R1C4 = 7 => R12C3 = 12 = {48}
or R1C4 = 9 => R4C1 = 2 => R3C12 = 16 = {79} => R12C3 = 10 = {28}
-> R12C3 = {28/48/58/68/78/89}, 8 locked for C3 and N1
9b. 18(3) cage at R5C3 (step 8d) = {279/369/459/567}, no 1
9c. 18(3) cage at R5C4 (step 8f) = {369/459/567}, no 1
9d. 1 in N7 only in R789C3, locked for C3
9e. 8 in R3 only in R3C589, CPE no 8 in R1C7
9f. 18(3) cage at R1C7 (step 8) = {189/279/369/378} (cannot be {468} because R1C7 only contains 1,2,3), no 4
9g. R1C7 = {123} -> no 1,3 in R2C6 + R3C5
10. 2 in N7 only in R7C1 + R89C3
10a. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 8 -> R12C3 + R4C1 = {48}4/{58}5/{68}6/{78}8/{89}9 (cannot be {28}2) which clashes with R7C1 + R89C3) -> no 2 in R12C3, no 2 in R4C1, clean-up: no 9 in R1C4 (step 3)
11. 18(3) cage at R1C7 (step 9a) = {189/279/369/378}
11a. Consider placement of 8 in N3
R2C7 = 8 => R3C5 = 8 (hidden single in R3) => 18(3) cage at R1C7 = {189/378}
or 8 in R3C89 => R2C7 = 3 => 18(3) cage at R1C7 = {189/279}
-> 18(3) cage at R1C7 = {189/279/378}, no 6
11b. Naked pair {79} in R26C6, locked for C6
11c. 18(3) cage at R2C7 (step 8b) = {189/369/378/468}
11d. 9 of {189/369} must be in R4C5 -> no 1,3 in R4C5
12. 18(3) cage at R1C7 (step 11a) = {189/279/378}, R4C6 + R5C5 + R6C4 (step 2a) = {126/234}, R5C5 + R6C6 (step 6g) = [49/67], 18(3) cage at R7C3 (step 7d) = {189/378}, 12(3) cage at R7C7 (step 6b) = {156/237/345}
12a. Consider combinations for R89C7 (step 6c) = {27/45}
R89C7 = {27}, locked for C7
or R89C7 = {45} => 12(3) cage at R7C7 = {237}, locked for D\, R6C6 = 9 => R5C5 = 4, R4C6 + R6C4 = {23}, locked for D/ -> R7C3 + R9C1 = [19], placed for D/ => R3C7 = 7
-> 7 in R3C7 + R89C7, locked for C7
12b. Consider placements for R1C7 = {123}
R1C7 = 1 => R2C6 + R3C5 = [98] => R2C7 = 8 (hidden single in N3)
or R1C7 = 2 => R89C7 = {45} => 12(3) cage at R7C7 = {237} => R7C7 = 3 => R2C7 = 8
or R1C7 = 3 => R2C7 = 8
-> R2C7 = 8
12c. R1C3 = 8 (hidden single in N1)
12d. R3C5 = 8 (hidden single in N2) -> R1C7 + R2C6 = [19/37]
12e. 2 in N3 only in R3C89, locked for R3
12f. 2 in N3 only in R3C89, CPE no 2 in R5C8
12g. 2 in N1 only in 12(3) cage at R1C1, locked for D\
12h. 12(3) cage at R1C1 (step 6e) = {129/237}, no 5,6
12i. 9 of {129} must be in R3C3 -> no 9 in R1C1 + R2C2
12j. 9 on D\ only in R3C3 + R6C6, CPE no 9 in R6C3
12k. 2 in N9 only in R89C6 = {27}, locked for C6 and N9
[The first key breakthrough; some 8s which were fairly easy in the normal Assassin have now been placed and R89C6 has been reduced to one combination.]
[As will be apparent from the diagonals the 7(2) cages at R1C2 and R8C9 must have different combinations as must the 13(2) cages at R1C8 and R8C1; but I didn’t find a way to use this.]
13. 12(3) cage at R1C1 = {129/237}, 12(3) cage at R7C7 = {156/345}, 18(3) cage at R1C9 = {459/567}, 18(3) cage at R7C3 = [189]/{378}, R4C6 + R5C5 + R6C4 = {126/234}, R5C5 + R6C6 = [49/76], 18(3) cage at R4C1 = {459/567}
13a. Consider combinations for 18(3) cage at R7C3 = [189]/{378}
18(3) cage at R7C1 = [189], placed for N7 and D/ => 13(2) cage at R8C1 = {67}, 18(3) cage at R1C9 = {567}, locked for D/ => {67}5 => R5C5 + R6C6 = [49], 9 placed for D\ => 12(3) cage at R1C1 = {237}, locked for N1 => 7(2) cage at R1C2 = {16} => caged X-Wing for 6 in 7(2) cage and 13(2) cage at R8C1, no other 6 in C12 => 18(3) cage at R3C1 = {459} = [495]
or 18(3) cage at R7C3 = {378}, locked for N7 and D/ => 13(2) cage at R8C1 = {49}, 18(3) cage at R1C9 = {459}, locked for D/ => R5C5 + R6C6 = [67], 7 placed for D\ => 12(3) cage at R1C1 = {129}, locked for N1 => 7(2) cage at R1C2 = {34} => caged X-Wing for 4 in 7(2) cage and 13(2) cage at R8C1, no other 4 in C12 => 18(3) cage at R3C1 = {567}
-> 18(3) cage at R3C1 = [495]/{567}, no 9 in R34C1, no 4 in R3C2 + R4C1, clean-up: no 2,7 in R1C4 (step 3)
13b. 19(3) cage at R1C3 = {478/568}
13c. 4 of {478} must be in R1C4 -> no 4 in R2C3
13d. 9 in N1 only in R3C23, locked for R3
[Now the same forcing chain from a different starting point, or I could have taken one of the previous ones further to a contradiction.]
14. Consider combinations for 18(3) cage at R3C1 = {459/567}
18(3) cage at R3C1 = {459} = [495] => R1C4 = 6 (step 3) => 7(2) cage at R1C2 = [16] => 18(3) cage at R1C9 = {459}
or 18(3) cage at R3C1 = {567} => 9 in N1 only in R3C3, placed for D\ => R5C5 + R6C6 = [67], 6 placed for D/ => 18(3) cage at R1C9 = {459}
-> 18(3) cage at R1C9 = {459}, locked for N3 and D\ -> R5C5 + R6C6 = [67], placed for D\
[Cracked. The rest is straightforward.]
14a. R5C5 = 6 -> R4C6 + R6C4 = 3 (step 2a) = {12}, locked for N5 and D/
14b. Naked pair {37} in R7C3 + R9C1, locked for N7, clean-up: no 6 in 13(2) cage at R8C1
14c. Naked pair {49} in 13(2) cage at R8C1, locked for N7
14d. 12(3) cage at R1C1 = {129} (only remaining combination) -> R3C3 = 9, R1C1 + R2C2 = {12}, locked for N1 and D\, clean-up: no 6 in 7(2) cage at R1C1
14e. Naked pair {34} in 7(2) cage at R1C2, locked for N1
14f. 7(2) cage at R8C9 = {16} (hidden pair in N9)
14g. 1 in R7 only in R7C456, locked for N8
14h. 4 in C3 only in R456C3, locked for N4
14i. 9 in C7 only in R45C7, locked for N6
15. R3C5 = 8 -> R1C7 + R2C6 = 10 = [19]
15a. 18(3) cage at R5C4 (step 8f) = {369/459} -> R5C4 = 9, R6C3 + R7C2 = [36/45], R4C5 = 4 -> R3C6 = 6 (cage sum)
15b. Naked pair {57} in R3C12, locked for R3, N1 and 18(3) cage at R3C1, R2C3 = 6 -> R1C4 = 5 (cage sum), R2C3 = 6
15c. R7C2 = 6 (hidden single in N7) -> R6C3 = 3
and the rest is naked singles, without using the diagonals.