I've never been to the BWCA so I can't comment directly on that. But another thing to consider, around the same area, would be the many state water trails in northern Minnesota. North central Minnesota, while full of lakes and rivers, is not heavily populated and while there are plenty of fishermen in the area I find it pretty easy to find lakes, rivers, and primitive campsites that are off the beaten path and a pleasure to paddle.
The Big Fork River is a beautiful and easy river to paddle. As I recall there are only two (possibly three) portages along the entire length. Only one of the portages is more than 20 meters and it's along easily traversed on roads in a small town (population 200). I've paddled it a few times and have never seen another boat.
There is also the Little Fork River, which I have not paddled. It has more whitewater and possibly more portages. I believe it's more water dependent as well.
There will be plenty of motorboats at times but Cutfoot Sioux lake is a very pretty area with a quiet full service campsite at the end of a short dirt road as well as paddle/walk in campsites as well. From Cutfoot sioux you can paddle into Little Cutfoot Sioux, then to Little Little Cutfoot Sioux, and from there into First River Flowage. These are all small lakes with plenty of shoreline to explore. There are some fishing resorts on a couple of the lakes but the farther you get down the chain of lakes the fewer the boats will be. There are primitive campsites along the way. I believe there is a campground on Little Cutfoot Sioux with shore access as well.
There are innumerable other lakes and rivers that offer similar exploration and might offer more solitude than a base camping lake in the BWCA.
Here is a link to the Minnesota Water Trails website. Many good paddling opportunities are not on it. Open a map and take a look.
Minnesota has 35 state water trails with over 4,500 miles of terrific paddling! Whether you want to kayak, canoe, or stay at a campsite on the river, you can find a place to paddle here.
www.dnr.state.mn.us