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.

"Seems to enter at PP I have to enter a lottery for BWCA. There must be someone I can talk to."

I don't think you have to get a Moose Lake permit that way - you would just do a self-serve? Day-use permit since you wouldn't be camping in BWCA that first day - unless you were using a "tow" in which case, the outfitters permit would cover your trip to PP on Day 1

Its been years (1996 or so?) since I've used Prairie Portage entry via Moose Lake, so I'm not an expert, but I think that's the way you would do it.  As to the BWCA permit for the return - I'd just see what is avaiable for the day you plan on crossing back to US side - or find a day with an open permit and pick that one to enter with - maybe it is just that "Entering form Canada" and I don't think they limit those? 

You really ought to call a BWCA Ranger Station and talk to them about it - or an outfitter, I suppose.  At least there is an advantage to camping the latter half of the trip in US - no fee other than the one time $15 as compared to $21.50 a day for the Quetico.

And I sorta doubt that IC's method is technically legal - as I seem to recall, once you leave BWCA for Quetico (or just a return to Ely for a day), you'd need a second/new BWCA permit to re-enter BWCA - can't go in and out as you please ?  but again, talk to the Forest Service people about it - the reservation people are likely just contractors or a concession I think, and may  or may not give you the correct answer

I think my method IS technically legal...I say I'm going in at Moose Lake on day X and leaving on day Y.  They don't care what I do in between as long as I pay the fee, go in the day I am supposed to, and leave around the estimated exit date.  I can't remember off hand how many days you can have on a permit but I think it is around 28-30 before you need to get a different permit. 

see "Travel Permits" below - copied from Forest Service  link below

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The following are enforceable Forest Service
regulations (maximum penalty of $5,000 and/or
6 months in jail).
TRAVEL PERMITS
• You must enter the BWCAW at the entry point
and on the entry date shown on your permit.
• You may not re-enter on a different date using
the same permit.
• Permit stubs become invalid when the trip leader
exits the wilderness.
GROUP SIZE
• Nine (9) people and four (4) watercraft are the
maximum allowed together in the wilderness.
• You may not exceed the limit at any time or
anywhere (on water, portages, campsites) in the
BWCAW.
• Smaller groups increase your wilderness
experience and decrease the impacts.
TOILET FACILITIES & WATER QUALITY
• Use latrines at designated campsites.
• Latrines are not garbage cans and should be used
for the intended purpose only. Personal waste
items such as cigarettes, cotton swabs, or plastic
feminine products should always be packed out
and should never go into the latrines.
• If you’re not near a latrine, dig a small hole 6 to
8 inches deep at least 150-200 feet or more back
from the water’s edge. When finished, fill hole
and cover with needles and leaves.
• Bathe and wash dishes at least 150-200 feet from
lakes and streams.
• All soaps pollute water including soaps labeled
“biodegradable.”
CONTAINERS
• Cans and glass bottles are not allowed.
• Containers of fuel, insect repellent, medicines,
personal toilet articles, and other items that are
not foods or beverages are the only cans and
bottles you may keep in their original containers.
• Food may be packaged in plastic containers that
must be packed out with you.
FOOD AND FISH REMAINS
• Try to plan your meals so you don’t have
leftovers. If you do, pack them out.
• Dispose of fish remains by traveling well away
from campsites, trails, portages and shorelines.
CAMPFIRES
• Fires are allowed within the steel fire grates at
designated campsites or as specifically approved
on your visitor’s permit.
• Bringing a small camp stove may be a better idea
because it heats food more quickly, has less
impact than a fire, and comes in handy during
rainy weather.
• Due to the potential fire danger, fire restrictions
may be put into effect. Check on current
conditions just prior to your trip. You may be
required to use a camp stove if there is a campfire
restriction.
• If you build a fire, burn only small diameter dead
wood found lying on the ground. Do not burn
trash.
BWCAWilderness Rules & Regulations
• Collect firewood away from campsites by
paddling down the shore and walking into
the woods where it is more abundant.
• Wood easily broken by hand or cut with a
small folding saw eliminates the need for
an axe.
• Drown your fire with water any time you
are going to be away from your camp or at
bedtime. Stir the ashes until they are cold
to the touch with a bare hand.
•

Its been a long time since I crossed the border by canoe, so I looked to see what kind of permits I was getting.  Going into Quetico thru Prairie Portage, I had a Moose Lake BWCA entry - just one, an overnight permit that had an entry date same as Day 1 for Quetico, and exit date for Day Last. Through Cache Bay, had a BWCA permit via Saganaga, and it was set up the same way, as an overnight permit with Day 1 as entry date and Day last as exit. So apparently that is how they issued the permits and make an exception to the no in and out rule for gong and coming to/from Quetico ?  or maybe it was Don't Ask Don't Tell ?  My last trip was in 94 - one way from Beaverhouse to Prairie Portage to Moose Lake - that one was set up by an outfitter, and the BWCA permit was for Entry 71 - Entry from Canada, and strangely, it also was an overnight permit with entry date being the same day we went in to Beaverhouse and exit day being Day Last even though we did not do anything more than paddle from PP to Moose Lake landing.

I'm thinking that there is no quota or limit to those Entry from Canada permits or it would be a logistical nightmare - so I'd think you could always get a day-use for Moose Lake, as an entry, and then the 71 for the time you wanted to come back across the border ?

at the bottom of that brochure I linked to, there are phone numbers for the BWCA ranger stations - I'd just give them a call and ask them how to go about it.  For me, I'd get the permits, but the boat registration thing would be a deal breaker today - back then, we always had my Dad's Grummans registered in NY for use with a motor (actually got checked on that by a MN Game Warden (or whatever he was) in a boat.