A lot for MT to sort out.  I think you can more easily break a BWCA trip into a before and after Quetico leg than the other way around, and if I'm not mistaken, you can use the same BWCA overnight paddle permit.  If you simply enter Q first, then a day paddle permit (or tow) and a "from Canada" for return, or get an overnight paddle to begin with.

The back and forth discussion is interesting as I asked Robin Reilly (at COPIA and at the time the superintendent of Q) about that, wanting to do a border trip and be able to camp on both sides.  He said it should be possible and seemed willing to make it work, but (ranger) Jason said no way.

Also I believe that several years ago they added a "base camp" permit that was not listed many times.  I still don't see it but twice I have used one and at last minute.  I seem to recall "Agnes Base Camp" was name and rangers grumbled that it was sort of a bastard permit.  Confirmed at PP last year they were still on the books and available.  I mention it because  it was offered as the correct choice for a short Basswood base camp permit, and they switched it at PP when I entered for my Sarah permit (so they could give the Sarah  permit to someone else and I had no intent of getting that far - 3 day trip.)

So, I'd go counterclockwise around Basswood, or maybe a figure 8, using a Basswood Falls entry and heading there for first night, then start clockwise circumnavigation, re-entering BWCA around Bayley or Inlet, and exiting through Jackfish.

If the less disclosed "base camp" permits are not available, what choice do you have for Q if you plan on no portaging other than Basswood Falls?  And I don't think hugging shore through North and Ranger and ending up at BW a week after entering park is in the spirit of the entry point and quota system.

Interesting planning challenge.