Thanks. Because the due has passed and no update is made (you have to carefully double check this), I think your file is to be updated by an officer. I think there are two scenarios here (1) either they have not received your security checks yet, (2) or if the security checks are done, your file is in line for the officer review. The only way to make sure if (1) is the case is to contact your MP probably and ask them specifically to check your file and "to see if your security checks are complete or in progress". You could also contact the call centre with a specific questions that "are my security checks complete" without any other additional questions. Unfortunately as per your experience the call centre may not really be checking your profile and may just give you a default "be patient " answer in an indirect way.
Although, some people may suggest against this, but I think talking with a lawyer would be definitely worth it as the last resource (may be after a few months from now)