I'm quite sure - from having asked the office and several rangers - you can leave and re-enter Quetico at will as long as you have a permit covering that time. So "stash" it at Dawson Creek or any place around the park, hitch a ride into Ely or Atikokan to shop, stay a night, whatever. They love you paying for nights not used!  Pay for 365 nights and come and go as you please.

I don't know the stash rule in the Q but I did learn in BWCA you can stash as during the duration of your permit. I don't see the reason this would not be allowed in Q.