You shouldn't need either a RABC or Quetico permit as long as you stay in the water or are on a portage trail running between the border lakes, i.e. the Bottle Portage from LLC to Bottle Lake/Iron Lake.  It's on the Canadian side, but you are legally entitled to traverse it without "officially" entering Canada.  I have forgotten the law/treaty stating such, and this is not considered legal advise, so you can dig a little further if you like.

However, I would make an effort to not fish the Canadian shores and bays, etc. that are obviously Canadian without a Ontario fishing permit, as the treaty allows for travel, not fishing.