OK I should not have completely trusted the documents. I found the answer after a couple of minutes, having tried it. The docs indicate that moreNavigationController is a read-only property. But this works fine for me:
tabBarController.moreNavigationController.navigationBar.barStyle = UIBarStyleBlackOpaque;
or
tabBarController.moreNavigationController.navigationBar.tintColor = [UIColor redColor];
In case someone wondered.
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