A 2x6 wall with R20 batts vinyls siding wood sheathing & siding and half-inch gypsum wallboard performs at about R14 whole-wall, after thermal bridging of the studs is factored in.
If you added 2" of Type II EPS (1.5lbs/cubic foot density, R4.2/inch @ 75F/24C, R4.5/inch @ 40F/4.4C- increasing as temps go lower). A 2" it would have about 1.5 perms of drying capacity toward the exterior, which is plenty, and it would bring your whole-wall R up to about R23 during the winter. If 3" you'd be down to 1 perm and R27-R28 whole wall (cutting your wall losses in half) which is starting to get pretty tight from a vapor permeance point of view but still OK under vinyl siding, which is inherently back-ventilated, and doesn't retain moisture (like masonry or fiber-cement can.) If you want to go even higher R with exterior foam you'd have to drop back to Type-I EPS (1lb nominal density) which can be a bit of a pain to deal with in a wall assembly since it's easily damaged.
Alternatively you could use rigid rock wool board (
Roxul ComfortBoard), which is nearly the same R/inch as EPS, but more than an order of magnitude higher vapor permeance. It's more expensive than EPS, but it's also completely fireproof, and there are no thickness limits from a vapor permeance point of view. You can get it as thick as 3" (R12), which is probably the practical limit from an installation- ease point of view.
At about R20 whole-wall the windows usually dominate the heat loss figures, so beyond the first 3" of exterior insulation you'll probably be getting more performance per loony out of something like low-E exterior storm windows on north, east and west sides (preserving the full solar gain of the south facing windows.) A tight low-T storm window drops the U-factor of a U-0.35 window to about U0.28-U0.30. It will bring a U0.30 window down near triple-pane sealed window performance.
The
low-E Larson storm windows sold through the blue & orange box stores are pretty good if you upgrade to the Silver or Gold series- the low end Bronze versions leak more air than you'd like in a high-performance house. A quick web search determined that the blue box store carries Larson.
The Larson dealer finder has a dozen or so hits of mostly the blue box store in the Toronto/Hamilton area- nothing close to Kenora, but you can probably still order them through the box-store even if they don't normally stock them.