Sorry to hear that. Yes, it takes months to gather all the evidence for your application. One possible avenue is to apply once you have all the core evidence, and you can always submit additional docs via webform later. This is what we did - our family doctor took ages to sign our reference letter so we submitted what we had and a month letter I added her letter as webform. There is of course risk that your file would be opened by the time you sent additional evidence and the officer may disregard the new piece (happened to us but on a different occasion - not with this letter). So I would try to gather as much as possible and not annoy officers by multiple submissions.
Also, an application going into process does not delay deportation. You have to get approval in principle (stage 1) to get CBSA off your shoulders. Of course, your CBSA officer may turn out to be nice and give you administrative deferral once you go into process, but this is not something that will happen automatically. Lots of hard work and patience needed. Good luck!