Jeremy -

If you have no objections to starting your trip on the northern side of Quetico, you can get an early start.  Ranger stations typically open at 8:00, so that doesn't typically facilitate a "first light" entry into the park.  However, if you head up to Atikokan, Ont (location of park headquarters), you can check in the day before your permit departure date and be on the water very early.  You could then enter at (West to East) Beaverhouse, Nym or French Lake (Dawson Creek).  Beaverhouse and French Lake put you in a position to do a lengthy paddle before anything beyond what I would consider a minimal portage would be involved.  Yet, that kind of area does tend to produce more travelers.  Nym, puts you in about mid-park and if you head generally south from there, you can get into some less traveled waters relatively soon.

Not only do the northern entries tend to draw fewer people than southern entry points, it is a bit simpler since you don't need a RABC (Remote Area Border Crossing permit) ... just a passport/passcard to get into Canada.  Nightly camping fees are a bit less also.

The earlier in May you go, the fewer the bugs (generally speaking).  June tends to be "max" bug month.  I do wear treated clothing (as described above).  The only repellant I take is as near to 100% deet as I can get ... which I wear sparingly.  If you can go before mid-May, you can get into the park before a permit is required.  If you go during this period, you need to be prepared for some "brisk" nights.  (I think my last year's trip--last 2 weeks in May--had maybe 3-4 days somewhere around 28 degrees overnight.)

dd