I'm just coming back from Radisson in Northern Québec. There is a road at the 274 km on the Trans Taïga that leads to Chibougamau. This road is 400 km of pure gravel. You cross some of the big rivers like the Rupert and the Eastmain.
One of the challenge will be refueling. The map that you show crosses many south-north roads that don't have any refueling point that far north. 400 or 500 km of autonomy seems to be the minimum at least in Quebec.
If you need any informations or help about the Quebec territory, just le me know. I and some friends pretty well know the territory.