What I have been told by the people in Idar-Oberstein is that generally, their beads are drilled from one side, with only few exceptions. So I would indeed like to see yours that appear to be Idar-Oberstein, but are drilled from both sides. And to see if the hole is also as big as the one posted first.
I remember us talking about the quality of the agate, and whether Idar-Oberstein was able to produce such high quality stones. To that, my answer is yes: they made very high quality cut agate beads, made from Brazilian agate.