I have a few scrambles planned in that area and did a bit of reconnaissance this past summer. The Oldman River road is in good shape until just past Oldman Falls, or about 500 m north of where Beehive Creek flows into the Oldman River, pretty much due east of Beehive Mountain. At that point there is a washout that is impassable in any vehicle (although a bike would work just fine). We were in our truck, but I remember thinking the car would have done just fine to the falls. The road continues past that point and may be slated for repair, but I'm not sure. Regardless, from the washout it's an easy day trip up Beehive Mountain, or a longish (26 km-ish) trip up Mount Lyall.
If you're thinking of heading into that area next summer let me know if you'd like company!