> It would refuse to chamfer or bevel edges for no apparent reason that other CAD software wouldn't have issues with.
I'm guessing you're trying to set a fillet which would completely consume one of the faces adjacent to the edge being filleted. In these cases I've found that a workaround is to make the fillet 0.001mm smaller than the size which would consume the entire face. You end up with a very very small amount of flat area but it's so small it doesn't show up during machining or 3d printing.
Usually the issue seemed to be with compound curves or where a filet tapers out as it meets up with a face going in another direction (such as a handle that sticks out).