I looked into this some years ago after taking the Agawa Canyon tour train from Saulte Ste Marie & seeing the territory.  Most of what I found were river trips, so not exactly like Quetico as I know it.  You can do an Agawa River trip, but I think it's organized & whitewater.
Sand River looked more appealing (start w/train from Frater to Sand Lake) -- still a river trip, but lots of fishing, etc from what I've read about (probably myccr).  I've been interested in the Mississagi River also - upstream from Rocky Island Lake (good info on myccr also & I've got a personal report from some guy in SSM).  You see the Mississagi R valley driving from Thessalon to Chapleau & it's quite beautiful -- the trip is upstream from the road, so quite a bit more remote.
I've wondered if Lake Superior PP has anything like that but haven't investigated.  People canoe some in Kilarney PP & it's beautiful, but pretty small.  How about Algonquin?  More people, marked portages, latrines, longer portages...but about same distance as SSM for you.

Good luck!  -Tom