Not with CX, but in the past I've definitely had to fight IB+ (and this is as an IB OWS elite) to correctly credit partner flights (from AY and BA, let alone CX)!

While I can't speak to your exact circumstances, with an E class ticket you should get your Avios and EP correctly. I would submit a new claim, but through email (or the complaints form) instead of via the missing Avios page. That way there's a paper trail with a specific reference number to refer to and you can question them directly rather than have them fob you off.

My last fight was earlier in May to get a BA flight credited (I'd been booked on an BA-oped IB codeshare but switched at the airport to an earlier BA-prime flight due to a delay) – I kept getting the automated "purchase conditions not met" email, which was obviously bs as it was a standard ticket and airport change, and it took about two months of back and forth on email before I finally saw them post.