Refitting Tillman battleships while retaining six-gun turrets

How would you refit a Tillman II or IV in 1925 to improve accuracy and rate of fire while retaining four six-gun turrets?

Fire each six-gun turret in groups of three or divide it into two triple arrangements. The proposed loading improvements become easier only if the requirement to retain every gun is relaxed.

Keeping every gun sharply limits the available remedies. Firing each six-gun mounting as two groups of three is proposed, with a possible internal division resembling the French approach to grouped guns. Reducing the mountings to triples or quadruples would create more room, but would breach the question's requirement. Experimental autoloaders are raised as another possibility. The later suggestion of fitting improved rammers or autoloading machinery into the large turret explicitly depends on reducing the gun count. No proven 1925 solution emerges for a mounting that retains all six guns.