Hi Lucas, at least you can sponsor, so that's not the problem. At this point, one can only guess.
I suggest that you ask for help from Eagle333, who supposedly has seen a lot of GCMS notes to help you. You can block out the personal information, and send it to him for him to give you some comments. (You can ask if it's ok, then email him...I think he also appreciates seeing more GCMS notes, so he gains more knowledge to help other people). You can check out another thread "GCMS notes as never explained before" and contact him. I don't think you need to worry about the acronyms.
You said you did not receive any emails to confirm that. So you confirm that Sponsorship has passed.
Let me try to walk you through a few things...this was how I read our notes.
Right in the beginning, Application: Fxxxxxxx. In this section, when was "Updated Date"? This gives an idea when the file was last touched. Then you find which section has been updated to see what the action was. In this section also, is it still "App status: Open", "App status reason: in progress"?
Then right after that, under "SPONSORSHIP - FAMILY CLASS AND REFUGEE", does it show "SPR Eligibility: Passed"? You said you never got email of SA. This is to double-check.
Then "ASSESSMENTS" which gives summary of various statuses: Eligibility, Security, Criminality, Medical. You Medical should be "passed" unless expired already. Eligibility, does it say "not started"?
Then "HISTORY" and also "ACTIVITY" sections, while there are not details here, you can see what has happened to your file, and when. Basically you can see when CIC has touched your file. If all the dates are old, then they did nothing for a long time, which hopefully you get some hints why in "NOTES" section.
Finally "NOTES" sections, this is where all the communications are. If you sent emails (but never got response), if CIC acted on them, they would put down what they did. Your MP making inquiries, they would also show up here. Any hints here?
My guess, guess only...your wife is missing some information which HKVO deemed need to be submitted before starting on her eligibility. But somehow, they have not asked you for it, so things are stuck. Your wife's situation could be the cause as you mentioned. As she did not have HK birth cert (my mom did not either, but that's because of after the war), and birth cert is required document, she would need her Hukou in China (my understanding is, Hukou is the key document in countries with Hukou system). Was that provided (I know, her Hukou would be cancelled upon immigrating to HK)? If yes, there's the difference in name spelling, so maybe that needs to be addressed somehow. And if your wife was after 18 when she moved to HK, she would also need to get her police cert from China.
Have you tried submitting a case specific inquiry to ask what's the problem and what could be missing?
Hope you sort this out soon.