Elranoc, I was having the same exact problem you were having. In order to find my initial PID frame, I hit my seed and advanced my frame about 12 consecutive times and listed each nature. Then, I repeated the entire process and compared/contrasted both lists to each other. Long story short, they were similar, but by no means identical:
List 1:
0 - Relaxed
1 - Relaxed
2 - Modest
3 - Modest
4 - Lonely
5 - Lonely
6 - Bashful
7 - Timid
8 - Gentle
9 - Relaxed
10 - Careful
List 2:
0 - Relaxed
1 - Relaxed
2 - Relaxed
3 - Modest
4 - Relaxed
5 - Lonely
6 - Timid
7 - Timid
8 - Gentle
9 - Relaxed
10 - Careful
Looking at my list of PID natures on the main page of RNG Reporter, I found this list of consecutive frames:
64 - Relaxed
65 - Relaxed
66 - Relaxed
67 - Modest
68 - Serious
69 - Timid
70 - Lonely
71 - Timid
72 - Relaxed
73 - Relaxed
74 - Relaxed
75 - Gentle
76 - Relaxed
77 - Careful
I noticed the discrepancies, but concluded that the lists were too close to be coincidence. Therefore, I started from 64 and advanced the PID to the amount needed to hit my perfect shiny spread. Fortunately for me, it worked after three attempts. You look like you're doing everything right, but my advice to you is to get a comprehensive list of PIDs (not just three or four) in order to get a more general overview of where your PID frame initializes. The lists I showed you also iterate that it will not be a perfect match, I assume due to the invisible movements of the NPCs off screen. It takes time, but don't give up and you will eventually hatch your peerfect shiny. Just my two cents, hope it helps.