I don't know if you found the answer or have already travelled, but this is my experience.
UA priority for Star members is a 9, which is the next highest after UA staff.
Airlines in the U.S. are generous and I have been lucky with C class.
In the Far East they go by the book. The Middle East is 50/50.
I fly Lufthansa quite a lot, but we have a C class Zed with them, so I buy a C class Zed to avoid disappointment. AA out of South America only board in Y, yet out of the USA I've had C. Out of Canada, never had anything but Y.
I think that these days, resign yourself to Y class travel unless you have the facility of purchasing C class Zed's, if you get C on any sector, it's a bonus and something to be thankfull for !