It's been ages since then but I favor the western half of the road, most especially when you head NW and get in the upper elevations. Ideally I would do it over a three day weekend. Start in Boise, hit the east end, camp somewhere west of Poison Creek. Camp again near the Oregon border. Go into Jordan Valley, refuel and take Cow Creek road into Silver City-over the summit and back to Murphy and home. If time was important, you could hit Hwy 95 at Jordan Valley and be back in Boise in 2.5 hrs.
You will not get over Silver City and NY summit before Memorial Day weekend due to snow. (They run a Cat through the big drifts the week prior to Memorial Day)