Why triple turrets would not greatly shorten the Admirals

Could the Admiral-class battlecruisers be shorter with three triple 15-inch turrets while retaining their speed?

Not by much: triple turrets require more beam, and shortening the hull would damage the length-to-beam ratio unless machinery power rose.

The wider barbettes and hull needed for triple turrets change the beam as well as the longitudinal layout. Speed depends on the resulting hull proportions, not merely the length occupied by magazines. Because the Admirals also require global range, simply forcing more power into a shorter hull is not an attractive solution.