Driver has the right idea, but the wrong product; what is needed is a product that goes by the tradename "Wiremold" or its equivalent. It's a form of wall-surface-mounted, decent-looking, paintable metallic conduit that will meet NEC requirements. The hollowed-out molding will not meet NEC req's. Wiremold sells pre-formed inner and outer corners, surface-mount outlet boxes and other useful accessories for successful completion of your "impossible" job.
BTW, I would have the electrician use STEEL (not aluminum) BX armored cable up to the point where you make the transition to the Wiremold because of its superior magnetic shielding properties.