Two very fascinating stories. I think military force was certainly effective in the Arkansas example, but would a visit by Eisenhower to Arkansas where Eisenhower attempted to convince Faubus that he was wrong have been effective? In short, I don't know. But I think that approach should have been attempted if it wasn't.
The situation with Darryl Davis and the KKK is completely different. Davis was not facing discrimination that was supported through state action. He was able to make a personal connection with KKK members, and this personal connection helped dismantle the entrenched racism that these KKK members had against black people. Perhaps a personal connection with a black person with the Faubus case would have worked to dismantle Faubus' racial animus, but it appears that his actions could also be motivated by what his constituents thought. Nonetheless, perhaps Eisenhower should have attempted a conversation before sending in the National Guard. Either way, his actions were effective and using the National Guard sent a strong message that the Federal Government was in support of dismantling a discriminatory system. Perhaps it was important to send that public message even if a personal conversation or a "gentler approach" had more potential to change "hearts and minds."