Help insetting an open subd into a solid to create a smooth solid subd

I am trying to inset the subd shown left into a solid. I can successfully boolean difference a mesh version of the shape from a solid (right), however, trying to quadremesh this into a subd eliminates the sharp corners I need. Applying guide curves also failed. In the end, I want a closed, smooth subd that looks like the shape on the right with the sharp corners of the original. Thank you for your help.

hard to help from a screenshot.
please post a file.

what are you going to do with the subD-result ?

it would be much easier to convert the subD to nurbs
_toNurbs
and then continue with nurbs-surfaces and end up with a closed polysurface.

kind regards -tom

Hi Tom,
The geometry is a mould that will be cnc milled (hence why I need a smooth inside surface with clear corners and a solid bounding box). Any rounded corners that are too acute will not be millable. I’ve tried closing the shape using nurbs, but have run into issues here too. Thanks for your help.
subd_questions.3dm (2.9 MB)

Please try to convert the SubD objct to Brep vis ToNURBS first, then run the BooleanDefference command , just fyi

This worked, thank you so much!