During the special parliamentary hearing 2010-07-27 at the Committee on Industry, Science and Technology, it was revealed that Statistics Canada had only the long-form census until the short-form census was introduced with statistical sampling in the mid-20th century.
The logical solution for high-accuracy census is to use the long-form census on every household, and scrap the short-form census. This will eliminate sampling errors altogether.
Even better, there should be a voluntary database for citizens to disclose answers to the census questions. Such a facility would act as a "permanent census" in which submission to Statistics Canada would be a push of a button after brief verification since most answers do no change over time.