Would a battlecruiser use 18- or 20-inch battleship guns, or retain a smaller battery to preserve speed?
Short answerIt would probably keep 15- or 16-inch guns unless the navy accepted a much larger hull, because the heavier mountings would threaten the speed requirement.
NotesThe G3's 16-inch armament gives a guide to the likely compromise. A battlecruiser designed to preserve speed cannot treat gun calibre independently from hull volume, machinery, and turret weight. Very large weapons consume space and displacement that might otherwise support speed. Unless the navy accepted a substantially larger ship, the fast design would probably retain smaller guns than contemporary battleships.