Akula -- Sadly, I think it will be the case: A popular entry point, in the middle of the summer -- I can't imagine anything but lots and lots of people.  But maybe that's not an issue with your group.

I've done Angleworm, and I agree it's a beast.  I've done Nina-Moose, and after being the middle of the hordes of people, I vowed never again.  

Maybe it's worth asking your group to pick its poison: 1) a helluva long portage, but less people, or 2) an easy entry point shared with seemingly most of the quarter-million people who flock to the BWCA each year!  I think I'd take Angleworm.  BUT, if you take Nina-Moose, and then look to get off the beaten path asap, that might be the way to go.  I've not  done that, so can't give you specific recommendations.

You're right, 4 days doesn't give you much time, no matter where you go.  However, I think the least used part of the BWCA is in the far northeast corner, the "Tip of the Angle," north of Grand Portage, around Pine Lake.  It's a longer drive, bigger lakes, longer portages, but I definitely felt more alone.  FWIW

prouboy