How the Deutschland design changes with its intended purpose

What armament would make a better follow-on to the Deutschland class?

For an efficient cruiser, nine 8-inch guns; for a treaty-stretching pre-dreadnought replacement, nine 11-inch guns.

A more efficient Deutschland-type cruiser would carry nine 8-inch guns instead of the historical six 11-inch weapons. The choice changes if Germany keeps the class's political role as a nominal replacement for old pre-dreadnoughts while already exceeding treaty limits. Under those assumptions, designers might as well exploit the displacement and fit nine 11-inch guns. The preferred armament follows the ship's intended mission and legal fiction as well as calibre.