If you haven't seen it already??? Check out my
trip report starting at Big Lake.
Big is a nice 'big' lake and, having visited it a few other times as well, the motor traffic was limited and did not ruin the experiences there.
I agree with egknuti, the river should be navigable. And, to speak with a little more detail about the portages.... The portage into Duck shouldn't cause too many problems. However, I would rate the Duck - Big Moose portage in my top 3 of all time toughest maintained portages in the BWCA. The silver lining may be because of how dry it has been recently the initial bog walk out of Duck may contain much less moisture and, thus, be a dryer/easier ordeal until you reach the big hill climbing out of the bog.
Big Moose is somewhat of an under used gem, simply because of the grueling portages to Duck and/or Cummings negate easy travel options.