It's an irritating problem and the only fix for a complex profile is to duplicate the profile and rotate it 90 degrees in the complex profile definition. You can then rotate it 90 degrees in the model and apply the angle on plan. It isn't a great solution & it isn't very BIM.
It should already be in the Wishlist to generate compound cuts (H&V) simultaneously. There is also a need for angled end cuts e.g. beams meeting in a corner. You could go down the Morph editing route, but again it's not a BIM or parametric solution.
Apple iMac macOS Sonoma / AC27UKI (most recent builds)