Aaron,

There's no good way to do it outside of French or Stanton.  

Kingfisher & MagicPaddler worked with Doug Chapman of Canadian Quetico Outfitters a few years back to obtain a special permit to use those logging roads to enter the park just north of Belaire.  They had hoped to access McKenzie Lake in one day.  Bottom line: it didn't happen in one day but they DID manage to - eventually - bushwhack in.

Any number of outfits will do the fly-in to Clay Lake.  From there it's potluck re: stream levels to get you to the Wawiag.  Seems like a high-water year (from the vantage point of the Twin Cities) but timing of a trip will make the difference if you attempt that route.  It works for most folks.

On an off & on basis, Quetico Park officials investigate "other" east entry options into Quetico.  I suspect they are years from developing anything.

Finally, allowing only five days to handle that rugged far eastern of the park means you will really be hopping around.  Fortunately, save McKenzie Lake, they are mostly smaller lakes where becoming "wind bound" is less of a factor (unless, of course, you plan a loop including Sturgeon & Pickerel; if THAT is the case, I say you are planning it a bit thin).

You know, I may have forgotten something here.  Seems to me that MagicPaddler has accessed the park via Mack Lake, somehow.  Maybe you can contact him to see how managed that.

Good luck!

Jimbo