You could probably try to get ATIP from CSIS. It is not very useful in general though, but it can tell if they have completed the checks or not. If they have completed the checks, I guess you should expect to hear from ircc soon.
On the Ircc ATIP what’s the status of your file? In the “note” section, does it mention which office is reviewing your case? Have you seen any recent historical update in the ATIP?
As your MP mentioned that the case in under review, there is a high chance that they have received the checks from csis but now ircc is reviewing the checks.