If that new world is a typical sword and sorcery place, those dudes should have no trouble finding girls right away. Don't they have a decent level of power already? Certainly, they would need to look for them outside of the royal castle, but who's forcing them to stay there? No, in fact, they might find interested maids in the castle. Many a maid would be an unmarried young woman. Once married, they would leave the job to become a housewife. The princess's "personal maid" might be in reality a lady-in-waiting, a daughter of a noble family, who wouldn't decide her own marriage partner, so those dudes would need to think twice before eyeing such a girl.