No idea what to advise as your bedtime is before your bolus insulin runs out. It could be you need more basal, it could be your ratio at dinner is wrong, or you could be going hypo at some point due to either of your insulins and rebounding without knowing it.
Maybe carb free dinner one night to see what your level does before bed? Then compare your morning reading. Other than that, it might be the dreaded, 12am, 3am, 6am tests to get an idea of what is going on. It is advised not to change overnight anything without knowing those numbers.