Any idea if this is a good idea even if your file is within normal processing times?
Law firms usually take citizenship cases at around 18-20 months of processing.
They argue that IRCC not meeting standard processing time of 12 months is causing excessive amount of problems for the applicants, but the delay should be at least a few month over that for them to believe that mandamus should succeed.
If you happen to be eligible for urgent processing, maybe try that route.
Otherwise, you can try calling IRCC, or contact your MP around the time you're past their average processing time, which is 18 months right now.
I just received my ATIP notes I ordered after the oath, and it looks like my attempts to contact them before starting the process of suing them in federal court actually resulted in some minor activity, they were checking my tax returns.