My dear By-Tor,
In my earlier life as a machinist, I learned to read engineering specifications and I acquired a certain feel for how bits and pieces might be persuaded to fit together.
Please bear in mind that not is all as it may appear: although a case may look "1:1" on the outside, to use the current jargon, it may very well be far from accurate on the inside.
It is so with many things in life, but I digress.
I believe the problem may lie with the relief given to the underside of the rehaut in the 1680 case. I have heard rumors elsewhere that one may simply machine away the underside of the rehaut ledge to create the correct clearances.
But that may just be the gin and tonic talking. Bottoms up!