Great info, Tiger!
OP asked about the 168 east of Bishop; would the OP consider White Mt rd, heading north from the 168 as it crosses the pass?
Depending on the OP's rig and his sense of adventure, he could try White Mt rd up to where it meets Silver Cyn, or at least to Grandview CG. Not sure what the status is of Grandview, or even whether the areas above Silver Canyon is still outsside of the Bristlecone protected area. But if it was me and I was headed that way, I'd get a gander at the magnificent views up there. And I'd have a look around at boondocking opportunites.
Grandview is/was maybe 5 miles up the road, Silver canyon another 5 or so. No guarantees!