For me, on these things, it seems prudent to begin with something gentle and get more aggressive only if needed.
Getting everything dry and brushing it all with a good stiff (I prefer synthetic) clean brush before vacuuming-up EVERYTHING that you loosen is always a first step -- this should remove any growing stuff as well as a lot of the spores. I use a synthetic brush that i know has been cleaned (ie: bleach soak) and dried to avoid spreading mold/mildew to anything else. For me, brushing dry and vacuuming should always come before any wet process just to assure that you're not helping the mold/mildem become more mobile and re-hydrated!
Secondly, I'd offer to go with a wet cleaning - good clear water, warm if you're OK with that; brush-scrub again (clean & stiff brush!)... as you start this, watch where the water goes; you'll wanna ensure that those area are well-dried and inspect them for mold/mildew as well. Let the whole thing dry completely.
If ther's staining or growth that one or two cycles of dry / wet scrubbing won't address, I'll reach for some Iosso Mold & Mildew Stain remover (also works on bird poop and leaf-stains) http://www.iosso.com .
Being in Washington, you may have better access to marine supply stores (better there than here, I'd imagine), which is where I first encountered the Iosso stuff -- A look at the boat-care items may turn up something else that's formulated especially for canvas that will leave the waterproofing intact... Should be worth a look
Also, if you're looking at products for cleaning, I don't believe the tent material is "canvas" in the old sense of the word. Certainly on the Leesurelite I had, it was more "plasticy" and there must be some sort of nylon or other sythetic involved. I think all modern tent and boat "canvas" is like that, but something to watch out for.
As well, you're near the Leesurelite factory in Osoyoos. Give them a call and they may have some advice.