Is it permissible to continue paying zakat to an organization that is known to differentiate between eligible recipients on the basis of nationality, given the difficulty of finding poor people or agents? And are the zakat payments previously made to that organization considered sufficient?

Entrusting a reliable entity with the distribution of Zakat (definition) is permissible, but it is not permissible to entrust it to an unreliable one. As long as the entrusted organization is known for its uprightness and trustworthiness, there is no blame upon you, and your obligation is discharged thereby. You are not required to re-distribute the Zakat, for the default is that Muslims are upright and trustworthy. However, it is preferable to distribute the Zakat yourself to ensure it reaches its rightful recipients. If the organization's betrayal is proven, your obligation is still discharged because they act in the place of the Imam's collectors, by whom the payer's obligation is discharged as soon as they receive the Zakat.