As far as I know, there's no story focusing specifically on Nanami and the Phantom Tribe. However in at least two stories, a significant subplot is set aside for something similar.
In Dooky's
The Shape of Things to Come, much of the story revolves around the efforts of a minority among the Phantom Tribe attempting to ally with and live within the Allied Nations. Parnasse eventually even hooks up with a cute Phantom Tribe girl, the lucky stiff.

In Mark Engels's and Ken Wolfe's
Rough Justice, a number of Phantom Tribe members live within the Allied Nations, as well, and one of them is married to Nanami. The lucky stiff.

In both cases, rather nasty racism is typically shown by the humans toward the Phantom immigrants.
You're right about Nanami seeming more positive toward the Phantom Tribe than anyone. On ALL THREE seperate occasions, upon meeting a member of the Phantom Tribe for the first time, she had something nice to say:
TO KURAYA: Your skin is beautiful.
TO NAHATO: How cute! It's a little Phantom Tribe boy!
TO GALUS: How cute! A marriage between the Phantom Tribe and the royal house!
That, plus her naturally immunity to the illusions of the Phantom Tribe, certainly make her a natural choice for bridging the gap between the embittered races of El-Hazard. Heck, her blood-ties to the military leader of the Bugrom might make her a good candidate for diplomacy there, too!
Or, maybe not.
