Hi - Sorry to hear you're facing these issues. It's hard to diagnose without seeing the file, if you're able to, please send us a stripped scene to helpdesk@itoosoft.com. That said, slicing at corners and elsewhere tends to result in cleaner geometry when the source objects are modelled primarily using quads. It gives you more control and leaves less guesswork to the resultant sliced mesh. I can't see your topology in the screenshots, but maybe adding some extra edges along the lengths of those moulded sections will help resolve this issue.
Many thanks,
Paul