Your permit is valid. My Washington permit has my Idaho address on it, I had the address updated before I made the move from Spokane to the Boise area. Washington will issue anyone (that's legal to have one) from any state and Idaho will recognize your Washington permit even if your a resident of Idaho.
I personally have decided not to get an Idaho regular or enhanced permit. Until Kalifornia and Oregon recognizes other states permits I just don't see the need for one. If you buy a firearm as an Idaho resident the NICS check is waived if you have an Idaho permit, but I don't see that as a big deal myself.
Open carry here in Idaho is real boring, haven't been bothered negatively yet, but have had many positive interactions with folks. I even opened carry in bars, no problems, it's legal to do so.