I can think of one particularly busy Q portage years ago that still puts my shoulders back, as in locked and loaded. Yeah, too many people can spoil things for sure. I'm not fond of seeing or hearing neighbors. I'll sometimes stay an extra day when I know I have a decent, off route, lake all to myself.
All things considered, IMO, for the time and expense of being dropped off on the one end of the park or getting a ride back, I'm thinking a loop back to your bike would make more sense $, time and effort wise.
You can find crowded portages in Quetico too but they'll normally be nearer entries and popular destination lakes. Paddling to the interior, turning left, and looping back to where you started would be just as, if not more remote all told. It doesn't sound as impressive as a one way, N to S route though does it?
If you want remote, study Beymer's book and go someplace else.
Now for the bad news:
Ever use a bolt cutters? I'd want my bike indoors or at the vary least out of site.
Youthful indiscretions? Really old things will come up for sure if you happen to qualify for a random(?) full background check. I don't know. I'd find out about any new considerations before shipping stuff to where you may not be able to access it. Consider the chances and repercussions. Hey, maybe drive to the other crossing and try your luck again or wait for a new shift....