That digital angle finder from Harbor Freight changed my life for crown molding. Caulk can hide gaps, but it often cracks over time and looks like a quick fix. Coping the inside corners is way more forgiving than trying to match weird angles. Your new geometry might be fun, but wait until the seasons change and all that caulk splits. I had to redo my living room after a year because the caulk shrank and looked terrible.