I don't know about number of days - I thought a BWCA permit was good for a year from entry - as long as you didn't "leave the wilderness".  (I doubt too many people stay that long and I therefore can’t confirm on Google - yet.)  When I looked into the border route and hopping back and forth, the only real problem was the Quetico permit - picking it up at a Ranger station on the day I entered - and having to leave the Q on the last day on the permit.  I wanted to do like 5 out of 10 days in Q but I would have to pay for the first to last whether I camped in Q every night or not.  Of course RABC, US immigration on way out, fishing paperwork for both countries if you fish, and the permits for both sides.

I wondered if you entered on Canadian side after going through immigration - no RABC - if you can cross into US and back and exit wilderness on Canadian side, since you would not be reporting to US immigration for a while.

We’re it me, I’d do all Q - lots of shore and bays and even opportunities to day hike.  And I’d probably squeal in a trip to Isabella - love paddling through the meadows leading up to it.  And Lost Bay is a nice paddle - protected if on a stormy day.  The old Ranger Bay ranger station is stabilized and an interesting walk about.  Lots to see from BF to PP along the Q side.