A faster Nelson with 15-inch guns

Could 15-inch/50 guns have saved enough weight to give the Nelson class more speed or another shaft?

The saved turret and ammunition weight could plausibly support an F3-like 28-knot design, perhaps without adding a third shaft.

Replacing nine 16-inch/45 guns with nine 15-inch/50 guns could save weight through differences in turret size and ammunition as well as the weapons themselves. The F3 design provides a comparison for a treaty-limited ship capable of about 28 knots. Its hull construction was less dense than Nelson's, placing it close to the boundary between a battlecruiser and a fast battleship. The Royal Navy apparently expected to transmit more power through two shafts, although the feasibility of that arrangement with contemporary metallurgy is questioned. The proposed speed therefore depends on several design changes and assumptions, rather than the gun-caliber reduction alone.