Thank you for the clear responses. Getting police certificates from Qatar (where we last lived before immigrating) is a hassle I'm keen to avoid! Does CIC care if I spent (say) 180 days there, i.e. close to the threshold of 183 days but numerically lower? Could that trigger secondary reviews, etc?
It's not public what exact elements in an application trigger closer scrutiny, so it's impossible to say with certainty. But I know of some people that spent quite a bit of time in one single country (over 5 months, but not enough to need to submit a police certificate) and their application went through without delay.
I myself would leave a bit more margin (say 170 days rather than 180, so you've got about two weeks of buffer), just to play it safe. Not so much out of a worry about possibly triggering a secondary review, but more to make sure I have some leeway in case I miscalculated time periods. And as an extra advantage: it'll likely keep away from any such conditional secondary reviews, too, should they exist.
And it means delaying the application by a week or two at most, compared to submitting at about 180 days.