You might be overestimating the Western Territories if you think the Xuan are that low. The Golden Fields are a wasteland, The Cai are the youngest Ducal clan, and the Western Territories are a wasteland ruled over by a Ducal clan barely any older than the Cai. You brought up how the Cai can't send family to the Imperial court, but the Sun also can't really do that either, they just lost Sun Lilling's aunt (great aunt?) who was their main voice at court and don't have anyone who can replace her. Those should be the 3 'weak' ducal clans. Then you've got the Bai who were kicked into the dirt recently but have ancient and strong foundations.
For Ducal clans in Imperial politics it probably goes-
1- Zheng (oldest and strongest, unchallenged #1, even if the throne wishes they could be reigned in)
2 & 3- Jin & Xuan probably in that order, but still roughly peers (strong established clans, the Jin are closer to mainstream imperial politics but the Xuan have a Sublime Ancestor)
4- Bai (Even at their weakest they're still very powerful and wealthy)
5, 6, & 7 (The Guo are better established than the Cai or Sun, but they rule a wasteland and their insularity means they lack both strong allies and enemies. The Cai are the newest and weakest Ducal clan, but the Emerald Seas aren't nearly as deadly as the other two so we're probably stronger economically. And Shenhua isn't exactly unpopular in the Peaks even with recent stuff going on. The Sun are barely any more established than the Cai, their territory was at least as hostile as the Golden Fields until recently, and their support in the Peaks was wanning, but they have a very strong army.)
The Savage Seas are among the half of the Imperial provinces that aren't recovering from some manner of recent catastrophe, I really doubt they're second from the bottom.