For a mirror-finish subject, you’re really lighting what the guitar reflects, not the guitar itself. The most useful approach is to surround it with a large white reflective/diffusing environment so the body sees broad, clean white shapes instead of bits of room, softbox edges, and black gaps.

A practical solution is a diffusion tent/light box or a curved white cyclorama made from white sheets, foam board, or similar material. Curve the background/sides rather than using flat panels so the reflections stay smooth and uninterrupted across the rounded chrome body. Then aim your lights at or through the tent/walls, not directly at the guitar.

Keep the camera shooting through the smallest opening possible so the lens/camera area doesn’t appear as a dark reflection.

If you want to refine your current setup, bring the softboxes in closer. That makes them effectively larger and softer, and can improve how the contours render. Using constant lights inside or with the softboxes can help you preview the reflections while adjusting placement.

So yes: a white tent or curved white surround is the smarter starting point, then tune contrast by changing how much white the guitar sees.