I spent some time today looking at some trails on google earth. It make the most sense to depart down the south-east portion of big bear mountain. There doesn't seem to be any maps from the OP's link. Im not very familiar with this area but, Im sure someone with knowledge of the area can chime in. I did find a link to a similar expedition from vegas, ending in johnson valley with a few gps waypoints.
Kawasaki Teryx Run from Las Vegas to Johnson Valley | UTV Guide
I was looking for a way to stay completely off road from big bear to johnson valley, but i was unable to find any. Although most roads out there are dirt...which i guess I could consider off road.