Thanks for the answers.
In the meantime I realized that I am a super dumb person. All of my previous calculations were wrong. I was putting the date I arrived to an overseas country, not the date I left Canada. There is 1 day difference and in total of 7 trips, this makes 7 days difference. I can no longer apply in May. But it is even worse: I am leaving Canada on June 4th for four months and according to the new calculation I meet the residency requirements on June 5th!!
I am fucking stupid, really. Perhaps I shouldn't apply at all. But I was wondering whether can I complete the application package and have a friend of mine sent it to CIC while I am away? This sounds reasonable to me now, but I lost faith in my ability to deal with these issues.