How appropriate would Walker Valley (in Washington State) be for a sport-touring bike (have V-STROM 650... upright tall bike, tires reputed to be not that great for dirt, I have had it on hard-packed forest roads and it handled fine for me). It is really only meant for hard-packed forest roads, and I am not sure if Walker Valley DNR area would be destination to try for my type of bike.
You probably won't like any of the trails, but there is a web of logging road of various quality.
The B-1000 road is the main line through the upper (eastern) portion and it does extend beyond Walker. You can access the B-1000 from the south end of Walker, where it reaches Lake Cavanaugh Road.