There are options. This preliminary report covers two of the most attractive and one partial solution.
It appears the Owner has a large space that was designed as Non-Conditioned workshop storage, and if converted to Conditioned, falls under the purview of Title 24, Part 6. The residential solution is to obtain an Energy Analysis and generally speaking attach 5/8" type "X" gypsum board to the underside of the trusses, assuming they are 24" on center. Then apply R30 batt insulation both at roof and ceiling and blanket insulate all ducts. It is important to vent the attic in this case. Since the studio appears to be subject to fire regulations similar to Santa Cruz Urban Wildland Iintermix Code (UWIC) (depending on local fire jurisdiction), it might have to be sprinklered if it ever goes to permit, and the local code might disallow eave vents. Therefore, employ large gable vents, sized appropriately for the attic square feet such as 1 sq ft net free area per 150 sq ft attic space. Considering the size of the structure, adding continuous ridge vents or pop-up vents would probably be necessary to provide sufficient ventilation with reasonably attractive gable vents. There would be some difficulty finding a roofing contractor that could perform all of the work without exposing the building to structural and fire scrutiny by authorities especially if neighbors trigger Code Compliance. Note this solution allows for existing Class B composition shingle, though even as white as you can get, the temperature rise will be minimum 50 degrees Fahrenheit over ambient, but that would be immaterial if all aspects of this solution are carried out.
A proposed solution falls more into the category of non-residential cool roof under Title 24, but it is important to retain the integrity of the existing 5/8" structural sheathing. The trusses will go wild if the sheathing is removed, and if that ever happens, Owner would have to re-roof to new design with new trusses or select another new system. Assuming the sheathing can be patched, it means possibly blanketing the underside of sheathing R33 batt foil side down (for winter); it might be possible to obtain a recommendation for foil side up for summer from an Energy Consultant. To the top of the sheathing apply rigid R-10; this is about all that is available. Then the metal roofing, which is generally galvanized sheet metal smooth white coating. The changes in roofing system must weigh the same as existing or structural work would have to be done. Note, the fire resistance of steel may be less than composition Class B, and its applicability for the stated purpose is unknown.
Owner might check with the planning jurisdiction (Napa County?) to see if they offer re-roofing guidelines when the proposed system varies from existing, probably the only case where a permit wouldn't normally be required. The fire jurisdiction might also offer useful guidelines. A planner or fire marshal should be able to offer reliable advice. The problem does appear to be soluble to the satisfaction of all concerned.
One other possibility is to consider incremental improvement. Re-roof with white fiberglass composition shingle or paint existing white. Inside, insulate underside with batt insulation. Call it done.