My start for Assassin 346 also applies for this variant apart from a couple of prelims and a couple of clean-ups, which have been omitted.
Prelims
a) R1C56 = {12}
b) R34C8 = {18/27/36/45}, no 9
c) R67C2 = {18/27/36/45}, no 9
d) R9C45 = {17/26/35}, no 4,8,9
e) 11(3) cage at R2C7 = {128/137/146/236/245}, no 9
f) 8(3) cage at R5C4 = {125/134}
g) 19(3) cage at R6C3 = {289/379/469/478/568}, no 1
h) 28(4) cage at R1C7 = {4789/5689}, no 1,2,3
i) 26(4) cage at R2C2 = {2789/3689/4589/4679/5678}, no 1
j) 26(4) cage at R6C4 = {2789/3689/4589/4679/5678}, no 1
k) 14(4) cage at R8C4 = {1238/1247/1256/1346/2345}, no 9
l) 37(7) cage at R1C1 = {1246789/1345789/2345689}
m) 37(7) cage at R7C9 = {1246789/1345789/2345689}
Steps resulting from Prelims
1a. Naked pair {12} in R1C56, locked for R1 and N2
1b. 8(3) cage at R5C4 = {125/134}, 1 locked for R5 and N5
1c. 28(4) cage at R1C7 = {4789/5689}, CPE no 8,9 in R1C4 + R2C789
1d. 3 in R1 only in R1C1234, locked for 37(7) cage at R1C1, no 3 in R23C1 + R2C4
1e. 37(7) cage must contain 8,9, CPE no 8,9 in R2C23
1f. Max R2C23 = 13 -> min R23C4 = 13, no 3 in R23C4
2. 45 rule on R1234 3 outies R5C239 = 23 = {689}, locked for R5
2a. 19(5) cage at R2C8 = {12349/12358/12367/13456} (cannot be {12457} because R5C9 only contains 6,8,9)
2b. R5C9 = {689} -> no 6,8,9 in R2C89 + R34C9
2c. 9 in N3 only in R1C789, locked for R1 and 28(4) cage at R1C7, no 9 in R2C6
2d. 24(4) cage at R4C3 = {1689/2589/2679/3489/3678/4569} (cannot be {3579/4578} because R5C23 contain two of 6,8,9)
2e. 1 of {1689} only in R4C3, other combinations only contain two of 6,8,9 -> no 6,8,9 in R4C3
3. 14(4) cage at R8C4 = {1247/2345} (cannot be {1238/1256/1346) which clash with R9C45), no 6,8
3a. 14(4) cage at R8C4 = {1247/2345}, CPE no 2,4 in R8C123 + R9C456, clean-up: no 6 in R9C45
3b. Combined 14(4) cage + R9C45 contain 1,3,5,7, CPE no 1,3,5,7 in R9C6
3c. 6,8,9 in R9 only in R9C6789, locked for 37(7) cage at R7C9, no 6,8,9 in R78C9 + R8C5
3d. 37(7) cage must contain 4, CPE no 4 in R8C78
3e. 37(7) cage contains 6 so must contain 2, CPE no 2 in R8C78
4. 45 rule on N36 4(2+2) outies R26C6 + R7C78 = 14
4a. Min R26C6 = 6 -> max R7C78 = 8, no 8,9 in R7C78
4b. Max R7C78 = 8 -> min R6C89 = 12, no 1,2 in R6C89
4c. Min R2C6 + R7C78 = 7 -> max R6C4 = 7
4d. Min R5C78 + R6C6 = {234} = 9 -> max R6C7 = 8
5. 3 in R1 only in 37(7) cage at R1C1 = {1345789/2345689}, 28(4) cage at R1C7 = {4789/5689}
5a. Hidden killer pair 6,7 in 37(7) cage and 28(4) cage for R1, each contains one of 6,7 -> they must be in R1 -> no 6,7 in R23C1 + R2C56
5b. 45 rule on R1 4(2+2 or 3+1) outies R23C1 + R2C56 = 23
5c. R23C1 must contain at least one of 1,2 for 37(7) cage -> max R23C1 = 11 -> min R2C56 = 12 -> R2C56 = {48/49/58/59} (cannot be {89} which clashes with 26(4) cage at R2C2)
5d. R2C56 = 12,13,14 -> R23C1 = 9,10,11 = {18/19/28/29}, no 4,5
5e. 26(4) cage at R2C2 = {4679/5678} (cannot be {2789/3689/4589} which clash with R2C56), no 2,3
5f. 26(4) cage and R2C56 ‘see’ each other so form combined cage {456789}, 26(4) cage = {4679/5678} -> R2C56 {58}/[94] = 13 -> R23C1 = 10 = {19/28}
5g. 37(7) cage must contain 4, locked for R1
5h. 37(7) cage and combined cage {456789} must both contain 4, locked for N12, no 4 in R3C2356
5i. Combined cage = {456789}, 8,9 locked for N2
5j. Max R3C56 = 13 -> min R4C56 = 12, no 2 in R4C56
5k. Hidden killer pair 1,2 in R23C1 and R3C23 for N1, R23C1 contains one of 1,2 -> R3C23 must contain one of 1,2
5l. 21(4) cage at R3C2 can only contain one of 1,2 -> no 1,2 in R4C12
[Since I’ve seen Ed’s WT for Assassin 346 and seen how powerful his step 2 was, it’s time to “borrow” that step for this puzzle. I ought to have spotted that 45, since I’d seen the one for R1234.]
6. 45 rule on C1234 4 outies R2679C5 = 1 innie R5C4 + 28
6a. Max R2679C5 = 30 -> max R5C4 = 2
6b. R2679C5 = 29,30 = {5789/6789}, 7,8,9 locked for C5, clean-up: no 5,7 in R9C4
6c. 25(4) cage at R3C5 = {3679/4579/4678} (cannot be {3589} because 8,9 only in R4C6) -> R3C6 = 7, R4C6 = {89}, clean-up: no 2 in R4C8
6d. Killer pair 5,6 in R2679C5 and R34C5, locked for C5
6e. 26(4) cage at R2C2 (step 5e) = {4679/5678}, 7 locked for R2 and N1
6f. 7 in R1 only in 28(4) cage at R1C7 = {4789) -> R2C6 = 4, R1C789 = {789}, 8 locked for R1 and N3, clean-up: no 1 in R4C8
6g. 26(4) cage = {5678}, 8 locked for C4, R2C5 = 9 (hidden single in N2), clean-up: no 1 in R23C1 (step 5f)
6h. Naked pair {28} in R23C1, locked for C1
6i. R3C23 = {19} (hidden pair in N1), locked for R3 and 21(4) cage at R3C2, clean-up: no 8 in R4C8
6j. R3C23 = {19} = 10 -> R4C12 = 11 = [38]/{47/56}, no 3 in R4C2
6k. 3 in R2 only in R2C789, locked for N3, clean-up: no 6 in R4C8
6l. R3C5 = 3 (hidden single in R3)
6m. R3C56 = [37] = 10 -> R4C56 = 15 = [69], clean-up: no 5 in R4C12
7. 45 rule on N47 4(2+2) outies R3C23 + R48C4 = 21, R3C23 = {19} = 10 -> R48C4 = 11 = {47} locked for C4
7a. R4C12 = [38] (cannot be {47} which clashes with R4C4), clean-up: no 6 in R3C8, no 1 in R6C2, no 1,6 in R7C2
7b. 9 in C1 only in 24(5) cage at R5C1 = {13479/13569} -> R8C2 = 3, 1 locked for C1, clean-up: no 6 in R6C2
7c. 14(4) cage at R8C4 = {1247} (only remaining combination), 1,2 locked for R9 and N7 -> R9C4 = 3, R9C5 = 5, R6C9 = 1 (hidden single in C1), clean-up: no 7 in R6C2
7d. R567C4 = [129] (hidden triple in C4), R8C1 = 9 (hidden single in C1), clean-up: no 7 in R7C2
7e. R5C45 = [14] -> R5C6 = 3 (cage sum)
7f. R8C4 = 4 (hidden single in N8), R9C1 = 7
7g. R4C4 = 7, R5C23 = {69} -> R4C3 = 2 (cage sum), clean-up: no 2 in R3C8
7h. R6C6 = 5, R5C78 = {27}, 7 locked for N6, R6C7 = 3 (cage sum)
7i. R6C3 = 7 (hidden single in N4), 8 in C3 only in 19(3) cage at R6C3 = [748]
7j. R6C89 = {69} (hidden pair in R6}, locked for N6
7k. R6C89 = {69} = 15 -> R7C78 = 5 = [23], R5C78 = [72]
7l. Naked pair {45} in R34C8, locked for C8
8. R2C8 = 1, R5C9 = 8 -> R234C9 = 10 = [325]
8a. 37(7) cage at R7C9 contains 6 so must contain 2 -> R8C5 = 2
8b. R67C5 = [87], R7C6 = 8 (hidden single in R7) -> R8C678 = 12 = [156]
and the rest is naked singles.