So, first off, you need to be sure to stay on top of the messages from CIC. I cannot stress this enough. If you want to finish the process and be successful, stay on them. Not to sound preachy here, but you can really put yourself at risk.
You can argue this one with CIC. Does ecas show that you have medical results? If so, and they have been received, then you can argue it. But for others, they chose not to. You do need to pick your battles here. If you know you'd pass, just do them.
You can contact CIC (webform is probably more useful, but you can back it up with a call into the call centre). You need to notify them that, in your region that you cannot get a medical done until April 12th. You've booked it on that date, as it was the soonest possible date you could get. We did have to contact CIC about a PCC that they claimed we needed (in error). I told them we have ordered it, but it may or may not be available by the date they requested. We cannot control what the embassy does with the request. There was no issue extending it. As long as you show that you are making the effort to placate them, they generally are ok.
That said, Can you make it to another region easily? Like some regions can do medicals the next day. I understand you are in NFLD, but other areas have doctors that can complete them sometimes next day (Kitchener is one said region). Sometime this is not possible, but if it's an option, then you may want to consider it. Can NS, PEI or NB do them sooner?