Oregon's law does not prohibit carrying your firearm loaded in a vehicle and specifically says firearms carried openly in belt holsters are not considered concealed.
None of the cities requiring unloaded carry without a CPL will be found in Eastern Oregon.
Your route should make you alright through Oregon.
Washington, however, does not recognize your Idaho permit and you will need to be unloaded while in the car or have it stowed.
Idaho honors ours but we do not return the favor for whatever reason our AG has.
Highly recommend you stop in Yakima or Seattle and apply for your Washington permit while you are here. Won't help you on this trip, but will on future trips into the state.