For citizenship purposes, I believe only basically government jobs qualify, and those essentially only ones where one is sent abroad as part of job - military, foreign affairs, some other very specific. You would know and what you are describing is not that. IIRC.I will be hired full time and working in Canada with extended on-site assignments (the IT lingo) but this is not for a foreign client and directly for the Canadian business that employs me and its customers who are out on pilgrimage. (boring) Part of my job will be documentation and admin tasks from the office here in Canada, stuff like getting visa documentation in order, hotel booking and things of that nature.
T4 is out of the picture completely then. I will discuss this with the lawyers now.