Is it permissible for me to use an intermediary to influence the girl's father to agree to the marriage, in the event of his refusal due to tribalism concerning lineage, and does this contradict Istikhara?

You were right in choosing a religious and moral girl. Since her father refuses your marriage because of ethnicity, there is no harm in seeking mediation from people to influence him to agree. This does not contradict Istikhara, for Istikhara is to follow the Sunnah of the Prophet, peace and blessings be upon him, and to achieve what is good, and this does not conflict with taking means to achieve a goal.