the 26.8mm goes farther down than the 27.2mm, but both seem to tighten up and stop well before the cage bolt area. now that you mention it, from the pic the seat tube does look like it's much narrower at the bottom bracket, than on the top.
It looks a bit like the one below, doesn't it? A Concept seat tube is straight when viewed from the side, and externally bulge-butted when looked at fore/aft.
I'm slightly surprised that a 27.2 will go in that one, but your problem is that the tube narrows, which is puzzling. Have you shone a torch down there to see if anything is revealed? I think lots of frames won't let you insert the post past the braze-ons, but aside from that they should generally be parallel-sided.
May I ask whether cutting the end off the 27.2 would be an acceptable solution?