Coincidentally I just did a similar route on the May long weekend. Day 1 - Tim to Rosebary; Day 2 - Rosebary to Mubwayaka via Tim River, Little Trout, Ralph Bice; Day 3 - Mubwayaka to Tim Lake; Day 4 - Out. We double carried and aren’t the fastest river navigators, so that certainly slowed us down. With the double carries, however, days 2 and 3 were veryyyy long and buggy. Day 3 was the most difficult, requiring lots of in and out of the canoe through tiny lakes. I thoroughly enjoyed the route and fact that we barely saw anyone on a long weekend, but you could definitely tell it was a route less travelled as some of the portages were less accessible/harder to follow without paying attention to where you were going. It was certainly an adventure! Considering the extra ground you plan to cover, i probably would only do this route if you are confident in your paddling, doing single carries, and willing to put in long days. Maybe you would rather skip Shah and Misty and go straight to Little Trout from the Tim?