I'll suggest 9mm:
6mm x 1.5 = 9mm
9mm x 1.5 = 13.5.
As for what's available near that... there's a Nagler 9mm, Delos 8 or 10, ES 82 degree 8.8mm or a monster 100 degree 9mm, Pentax XW10, Nikon 10SW, Vixen LVW8 or Vixen SSW 10.
Spoiled for choice I suggest. Your call.
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