I don't see the problem, you may see in many videos how glass is smoothly perforated and smoothly cut: https://www.youtube.com/watch?v=a_qMKKwvzz8 , but if they cant... no problem, if the pin is retained by the metal plating then the glass hole may be larger than the pin:
In my case, cutting the two glasses will be under $20, I often rent that machine for some $200/h, and if you see the videos this can be done in less than 5min.
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This is my reviewed design, the idea is placing a punched sandwich and then tensioning the left plate before tightening the (not shown) bolts, so the good inter pin distance will be adjusted:
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