To answer your first question, at least some of the outfitters in Ely are reported to shuttle to Beaverhouse.  Piragis has been mentioned as one that would.  I thought it was in the $150 range but could be terribly off.  So call a few outfitters - maybe one you have done business with - and see  if they will and if you can afford it.  Least expensive would seem to be one of your party drives up day before and the outfitter follows or leaves a little after you and shuttles that driver back to Ely.  I'm sure more expensive would be to have them position your car there since that would take two drivers or I suppose you could time it and a driver would return with you to Ely.  The plainest and most straight forward is they meet and shuttle you back to Ely to your car, which I'm sure they'll move to Ely from Moose or your BWCAW EP at little additional to the Beaverhouse shuttle.