It's a very realistic route, nothing too crazy about it. Your last day could be challenging if there are heavy winds. In late August it took me around 9 hours to get from Little Otterslide down to Canoe Lake because of the wind. My canoe was bouncing up and down during the final paddle on Canoe Lake, the waves were crazy.
If you're camping on Burnt Island though, if the forecast is calling for bad winds you can try to get a campsite on the western side of the lake, to make your final day shorter. Hitting the water early, you would only need to deal with wind on Joe and Canoe, so it wouldn't be too bad.
I've camped on Little Otterslide more times that I have Otterslide, but I do prefer Otterslide as the destination lake. I find the campsites are overall nicer and with prettier views. I always advocate for rest days but if the forecast looks promising before the trip and you want to drop the rest day, you can consider Sunbeam > Big Trout > Otterslide > Burnt Island. Either way I personally wouldn't spend two nights on Burnt Island... even in September it will be very busy and the campsites are not as nice as the other lakes on your route. If you keep the rest day, I'd personally use it on Big Trout instead. Sunbeam > Big Trout x2 > Burnt Island.
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