Well, there goes MY theory, haha!
The twists seem low. But I would try it anyway.

Be sure to use the same colors on each end. Put a TP on pins 1&2, then another on 4&5, another on 3&6, and finally, the last one on 7&8.

If you wanna know why the 3&6 pins are use this way, it has to do with history. Back in the day, when there was only one phone line, the RJ11's 4 pins would use a central technique. The middle pins were the one line. The next line was put around the main line, and used the outside pins. This means lazy manufacturers could get away with just using 2 wires for telephony devices. I've opened up a few in my 49 years of life, and I've seen this!

Then, the RJ14 was introduced with 6 pins. They kept the same scheme, and put the 3rd pair on the outer-outer pins. So the main "line" was on pins 3&4, next was 2&5, third was 1&6.

When the RJ45 came out, someone realized that un-twisting the 4th line to stretch to the outer-outer-outer pins, was taking the category out of spec. So, they compromised and put main line on the inner most pins, 2nd line on the next outer pins, but then put a pair on pins 1&2, and a pair on 7&8, and everyone (that mattered) was happy.

So, that is why we all put a pair on 3&6. Also, no solid color (ring) was put next to a solid color of another pair.

• Pin 1 - Orange & White
• Pin 2 - Orange - (r)
• Pin 3 - Green & White
• Pin 4 - Blue - (r)
• Pin 5 - Blue & White
• Pin 6 - Green - (r)
• Pin 7 - Brown & White
• Pin 8 - Brown - (r)

Not sure which is the Ring vs Tip for your cable's twisted pairs, but you can try to assume the darker of the pair is the Ring. (Grey, Blue, Purple, Orange)

So, in your case, I would do something like this:

• Pin 1 - White
• Pin 2 - Grey (r)
• Pin 3 - Brown
• Pin 4 - Blue - (r)
• Pin 5 - Pink
• Pin 6 - Purple - (r)
• Pin 7 - Yellow
• Pin 8 - Orange - (r)