Maybe the White Sword Tower can be made an upgrade of the Red Keep instead of a separate building in itself, automatically added when Aegon does the "Create Kingsguard" decision. So for the sixth building in KIng's Landing, perhaps a city called "KIng's Landing Harbour." (Lys already has a holding called their harbour) In A Clash of Kings, I remember Tyrion had to destroy a series of trading huts and buildings outside the Mud Gate so the defenders could shoot at Stannis' attackers easier.
As for my proposed White Sword tower, maybe this can be a seventh addition to the defence upgrades. It could add one or two more layers of defence and perhaps some more heavy cavalry for the Red Keep, since I would assume the Kingsguard would go into battle on horse, and not foot. That, and their knights armed and armoured by the crown, not some poor dude farmer with a horse called to arms by his liege-lord.