If one were wanting to plan a trip to get away from the crowds, where would one want to go?

Beaver Adams and Boulder

It's a little bit of a crapshoot at any given point in time, but Bulldogge's suggestion has good odds, as well as the small lakes north of there - Cap, Ledge . . . Hoe. Also pretty quiet between the Frost River and Louse River - Hub, Mesaba, Wine, etc.

Another possibility is the loop of small lakes south of LLC between Little Loon and Rocky - Slim, Steep, Finger, Gebe or Gun, Tacukmich, Trillium.

East end of Saganagons, Quetico.

And the PMA's while a bit of work, should provide solitude.
Before BWCA.com the way we would seek solitude is cross long and difficult portages.

Quetico in late August has always made us feel we were the only people around (and we like it that way!)
TZ

Often, back bays will have one camp and if you can snag it, you may not even have to over travel to achieve a good solitude you want. You may have to plant a bright yellow chair or other identification which can be seen from a distance to discourage others from coming too close. Could be worth the trouble.

Look at areas outside of BWCA and Quetico.

Quetico is my first choice, in the BWCA , Buck and Western Lake area would be worth looking at,

September is good for solitude...on Slim last year I only saw people 2x- paddling in and on the portage coming out.

Bulldogge and bonnie had some very good suggestions but I think you can find solitude just about any location in the BW that you portage, portage, portage to get there. The longer the portages the better. Early and late season also help.

UPBoy

Wine Lake.

The Lujenida to Zenith portage tends to keep a lot of people away.

Head south on the Indian Sioux to Bootleg Lake. Only one permit issued every other day.

We had good luck with Crab Lake, EP4, last August. The portages are long, which is part of what keeps the crowds away.

singlebladecanoe: "If one were wanting to plan a trip to get away from the crowds, where would one want to go?"

Bulldogge62: "Beaver Adams and Boulder"

Indeed!!! Yes indeed.

Late September/Early October a couple portages in on a dead end lake will almost always be empty