Pilou,

After a boolean cutting, inset is not a so bad idea.

You could "inset" two or three faces of a solid together to avoid part of the corner problem you had.

For external corner you select together 3 faces, for external egdes, 2 faces and top internal face only one.

 

Perhaps another way is

-- Copy/paste original solid
-- a boolean cutting with lines
-- explodemove function on cutted solids
-- your copy is inner solid and have to be resized

The problem is : with ExplodeMove you don't have spaces not so regular.