Congratulations! What is your timeline?
They may ask you for a re-medical if your BGC takes longer and they choose not to extend your medicals.... it's a tricky situation! If you ask for an extension, it may delay your process and put you back in line until they decide to re-open your file next.
My suggestion is to wait for the BG process to get done, and then take a call on whether to write back to them asking if medicals can be extended by a month or two -- and if you can submit a new medical as you can't travel in January (lay out your reasons clearly). It is still a risk as they may just delay your whole process if they are not convinced. Are you sure you cannot fly to Canada in January?
Others may have a better suggestion, I honestly wouldn't delay the process at all unless there are very cogent, non negotiable reasons for not landing in Canada before your COPR expires.
