Thanks pafurijaz, your files were quite helpful to check out different options, but in the end, none of them was viable.
I'll probably have to bite the bullet and update to Rhino 7, they now have Subdivision Surfaces implemented pretty perfectly.
I'm not a big fan of Rhino, but it is getting stuff done, even if clumsy.
And thanks Michael for looking into it, but since my job starts next week, I guess I'll have to find other solutions... ;-)
This is a cube in Blender with some of the edges (the pink ones) set to a crease value of 1.0, which is fully sharp. At 0.0, which means no creasing, the object would be a sphere. Then gradually the creases become more and more sharp.
As you can see, the lower frontal corner has three sharp creases come together, so it forms a sharp, pointed corner, basically like in the original cube:
Now to get sharp corners in MoI, those creased edges need to be split:
This results in each polygon getting it's own rounding instead of meeting in the pointed corner - the open edges work only where two corners meet like in the upper right area:
And the same happens if I import that open edge object into MoI:
So what would be needed is a different way to tell the object/MoI on import what edges should be sharp (or in an ideal world it would be like in Blender a weight per edge between 0.0 and 1.0 for in-between semi-sharpness).
This could for instance be done in a window like the export windows you use for polygonal export, where the wireframe of the imported file is shown and the user can select edges and assign weights.
Subdivision Surfaces are only really useful if there is edge-weighting, otherwise it's only usable for some edge cases.
For completeness, here I set the edge weights that were 1.0 before to 0.8:
This is often very nice for slightly rounded corners and semi-organic shapes that have a very special kind of natural behaviour:

This look can be achieved by the methods pafurijaz showed, by having the semi-sharp edges have double-edges that either coincide or have a slight distance for larger roundings.
That was the old method we were using back in ~2000 in Lightwave 3D, before there was edge weighting.
It works in most cases, but creates very messy meshes that are hard to work with, since the overlapping edges can't be easily changed once they are created.
Blender has it implemented very well, Softimage XSI had it down to perfection and most polygon-modellers do it well for quite a while, Rhino 7 only offers sharp edges, no in-between weights, but they do it mathematically perfect, so it can be used like NURBS and converted easily.
I'll also attach the blender file and the obj.
Cheers,
Tom