Success! It does just fit on the rails without disturbing the saddle position
Good, similar to the fit on my Audax bike
I was thinking that your saddle looked fairly far back on the post, and that there ought to be space depending on the design of the saddle clamp.
They might have sorted the issue out now, but it has been the case that the grub screws in the Bagman are a bit prone to loosening off: proper Allen head bolts resolve the issue.