Look at Google Earth. Southern Indian Lake is over 250 m asl. The lower Churchill is not a long lake - the Churchill is one of the larger rivers in North America, which was rarely canoed before the diversion (too much water/rapids). You'd think it'd be more popular now - I wouldn't call the lower Churchill uninteresting. (I've been on both the upper Seal and lower Churchill).
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I've heard more than one story about someone dying crossing Button Bay west of Churchill, and have seen a paddling presentation about the crossing. I recall scenes of them camping on a tiny plot of grass, only a few inches above the waves (hoping the waves didn't build any higher). Someone also stood guard to ward off the polar bears in the area. The shoreline has a very low relief, so if the wind/waves come up, it's not easy to get to safety. I wouldn't make the trip.
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There's a good guidebook for the Seal, and the route is a lot shorter, and the access via Tadoule easier (I've flown in commerical with a pakboat, but your kayak may be more problematic). You may be able to get a shuttle to Churchill like Recped did.
The route from Leaf route is significantly longer, and there's no guidebook. Here's an online resource I found Googling:
http://www.forgey-cabin.com/1972canoeexpedition.html. (The author eventually bought a cabin on the lower Churchill River, and wrote multiple wilderness medicine guidebooks.) There's also a published account in a book by Bill Rom titled
Canoe Country Wilderness.
People canoe the Knife as well.