Could Scharnhorst still use 11-inch guns?

Would a later Scharnhorst class still use 11-inch guns, perhaps in four triple turrets?

Probably, because German infrastructure remains the binding constraint, though the ships would look less competitive against the new cruiser category.

German design is constrained more by damaged infrastructure than by what rival navies would ideally demand. Building a weapon larger than 11 inches would require another year to eighteen months of delay or divert money from other research. Germany may retain the smaller guns because they are what it can produce. The new international population of 9.2- and 10-inch cruisers would make that choice look much less formidable.