In these types of conditions and for a parking lot (not highly important to get 95 percent) where a stable condition is needed and no significant ruts before placing base course, I have changed the plan and use a coarse quarry rock fill, what we call "breaker run". This works well over unstable areas as the only fill.
Sometimes it is possible to stabilize the situation using rock fill that we call 3" clear, the same stuff as breaker run, but with no fines below the 3 inch size. In this case this is placed over the unstable area and compacted into the lower mushy material and the fines are driven into the voids of this rocky fill. With enough of the rock, things stabilize since all loads are carried rock to rock.
When it comes to design, however, I consider any stabilizing layer as just subgrade, not base course material.
There are other treatments that may be considered, such as stabilizing with lime or old cement.