Just kidding!!! I think your ptoblem is the black piece at 12:00. You are using a load spreader plus the black support. Since you are using a load spreader you don’t need that black support. It takes up space. Someone else had the same problem. They removed the black support and had more room to clamp the cross.
I never tried the strings in badminton but do it for tennis now all the time. Same concept as you when you weave your crosses you start up or down so when I am doing tennis rackets and I come across a covered hole if I am weaving up, my cross goes under the covered hole and when I come out I go over the covered hole and vice versa. This gives me a hard weave and less movement on my cross. Luckily for the pattern I use on Yonex rackets, when I come across the covered crosses when I go through under the shared hole my cross starts up and out it goes over the staggered holes. Another thing I might do especially with high tensions I would use my grommet grinder and give those covered crosses a quarter turn to make sure there is space for my cross to go through.
I hope I figured out your problem =)
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