Lots of recommendations for the solo option, but I guess it's no surprise because many on this forum typically travel solo.  I guess this could be a good trip to try out solo paddling, but I'd recommend a trial run on a lake near your home.  That way, if you hate it, you're not stuck for several days.

Although I'd love to try it, I have not paddled a solo canoe, but don't mind soloing in a tandem canoe.  If you decide on 3 people to one canoe, I'd highly recommend the Souris River 18.5' with 3rd seat.  Many outfitters in Ely have it, and it's very spacious and comfortable for 3 people.  Frankly, 3 people to a canoe is my prefered travel method, as it helps with single or 1.5 portaging.  I dislike a group size of 7 the most.  With all 3 people paddling, a canoe will flat out fly, even in a headwind.  However, fishing while traveling does indeed pose a challenge.  Since a few members of our regular group don't fish, have no interest in fishing, and don't even really like the taste of fish (heresy, I know!) it isn't a problem.  They get to relax in camp, explore the woods, catch up on reading, or whatever else they like to do.  Meanwhile, we have enough canoes to have 2 fishers in each, and our travel speed means we have a lot of time to fish once we get to camp.  Just take stock of your group's personalities, abilities and goals to make your decision.