Responses
Well it does say nobody ever found out that the Emperor's shadow existed and it's doubtful it would be documented, much less something people would go looking for since there's no knowledge of it. Also the imperial harem does exist in Chinese history so it's also likely Kansei took on some concubines and had children with them, those would be of imperial blood. To combat the conflict of "the eldest will be heir" Shou and the princess' children just need to be born after Kansei's
Wait, so the princess ended up w Kansei?