Hi! Just a quick note regarding your timeline: 1 year and 7 months is actually much longer than the standard average. For most applicants, the medical exam (IME) or its request typically comes around 1 year (plus-minus a couple of months) after submission.
As for doing it proactively: no, you shouldn't do the medical exam without an official request from IRCC. If you do it upfront on your own initiative, the panel physician's clinic won't have a specific IME number linked to your active application file, and it will be very difficult (sometimes impossible) to properly attach those results to your case. It's always best to wait for the official instruction letter.
!! It really frustrates me because it was by far the most reliable tool. Now, the only tool is GCKey, and it’s completely out of date. For example, it still says that they’re assessing eligibility, even though the tracker showed that this stage had already been completed for more than a year before it went down.