So I now have a dilemma, as this seems to be a rare size indeed...
31.8 and widen it a bit, or 34.9 and tighten it a lot?
Indeed, it does appear to be a strange size. I measured it across the fore-and-aft and 'athwartships' axes, just to be certain.
In my case, the shim I'm using appears to be about 0,5mm thick Au sheet, which would imply an increase of roughly 1mm, which suggests that the internal diameter of my clamp is most likely to be 34,9.
I'll happily re-measure it if you like, including the non-compressed internal diameter of the clamp, to be certain.
What I can say is that it's been like that since (ISTR) around 1996 and I've never had any problems with it at all. Until I opened it up the other day I wasn't even aware that there was a shim in there!
btw... Post some pictures of your 8000, please! I'm still curious about why these apparently very good bikes appear to be so uncommon or to have so little kudos.