Khriss's letter is quite old (it predates Patji coming to First of the Sun at least), we canonot be sure FotS is still the only planet with a perpendicularity on it's system. This being said Obrodai was recently claimed by ambition and perpendicularity appears to need time to develop so it would probably need to have had a perpendicularity beforehand
Sixth of the dusk is set in Mistborn era 4 but the letters are set at the latest in the Stormlight era and it would be surprising he has obtained a mini-perpendicularity in the 70years between Mistborn era 1 and Stormlight
And FotS cannot be Obrodai because Patji wouldn't have to put a specialy-made avatar of Ambition to protect FotS from Hoid (Patji would have be far enough) and she needed one for Obrodai
