For example, would something like taking the sheetrock down (see what is behind it) and possibly add some vapor barriers with a thin airgap between the roof and the conditioned space. I guess similar to firring strips?
That’s pretty much it. If you’re willing to go to the trouble, remove the wood soffit and replace it with vented, put in a wood fascia, tear out the ceiling from the inside, create an airspace that goes right up to the ridge and vents out the top, then rebuild the ceiling
You want it to go from outside-in: roof deck, ventilation, insulation, vapor barrier, interior finish. How much space you’re willing it lose vs how much insulation and air space is up to you. Again, my experience is building in cold climates, not wet ones