How about a simpler input, with a solution we can compare against
depth: 510
target: 11,16
Expected time to reach 11,16 is 52. Here is a possible solution to reach 11,16.
x 0 y 0 ( rocky) w/ torch @ t= 0
x 0 y 1 ( rocky) w/ torch @ t= 1
x 1 y 1 (narrow) w/ torch @ t= 2
x 1 y 1 (narrow) w/ none @ t= 9
x 2 y 1 ( wet) w/ none @ t=10
x 3 y 1 (narrow) w/ none @ t=11
x 4 y 1 ( wet) w/ none @ t=12
x 4 y 1 ( wet) w/ climbing @ t=19
x 4 y 2 ( rocky) w/ climbing @ t=20
x 4 y 3 ( rocky) w/ climbing @ t=21
x 4 y 4 ( wet) w/ climbing @ t=22
x 4 y 5 ( wet) w/ climbing @ t=23
x 4 y 6 ( wet) w/ climbing @ t=24
x 4 y 7 ( wet) w/ climbing @ t=25
x 4 y 8 ( wet) w/ climbing @ t=26
x 4 y 9 ( wet) w/ climbing @ t=27
x 5 y 9 ( wet) w/ climbing @ t=28
x 5 y 10 ( wet) w/ climbing @ t=29
x 5 y 11 ( rocky) w/ climbing @ t=30
x 5 y 12 ( rocky) w/ climbing @ t=31
x 6 y 12 ( wet) w/ climbing @ t=32
x 7 y 12 ( rocky) w/ climbing @ t=33
x 8 y 12 ( rocky) w/ climbing @ t=34
x 9 y 12 ( wet) w/ climbing @ t=35
x 9 y 13 ( wet) w/ climbing @ t=36
x 10 y 13 ( wet) w/ climbing @ t=37
x 11 y 13 ( rocky) w/ climbing @ t=38
x 11 y 13 ( rocky) w/ torch @ t=45
x 11 y 14 (narrow) w/ torch @ t=46
x 12 y 14 (narrow) w/ torch @ t=47
x 13 y 14 (narrow) w/ torch @ t=48
x 13 y 15 ( rocky) w/ torch @ t=49
x 13 y 16 (narrow) w/ torch @ t=50
x 12 y 16 (narrow) w/ torch @ t=51
x 11 y 16 ( rocky) w/ torch @ t=52
If your code says something different, perhaps you could have it produce similar output for the path it tries to take, and then it is possible to discuss where it differs from an optimal solution.