Shorter time trip, you could stay on Pickeral with no  portages;

5 to 7 days would make a nice liesurely one-way trip from Beaverhouse across the northern tier of lakes, and exit at either Nym or French - that would require a shuttle though.  Beaverhouse to Nym is maybe 2 to 3 days travel, doing it in a week would leave lots of time for fishing and an easy pace.

My personal choice would be Start at French, down thru the "B's to Oliphaunt and Sturgeon, and return via Dieux Riviers (or however its spelled)  Most portages are reasonably short, with only the one long portage between Fern and Oliphaunt - if you make that a one day trip - i.e. camp on Fern one night, and on Oliphaunt the next, you could take your time on the portage.

IF you are planning on late summer, then some of the small creek travel may be a poor choice, such as Dieux Riviere, which can get too low for easy travel.