In support to DOC's suggestion, you could attend a Cong some distance away from the territory where you actually moved to. Attend a few meetings on an irregular basis but request to have your publisher card moved there.
Claim a job transfer requires some evening and weekend training which may result in irregular attendance initially. If asked for your address, claim you currently reside in a temporary apt/house until you find something more suitable and permanent.
Since you mentioned moving yet again, it won't be too odd initially when you don't further attend. They will then probably expect to receive a request to further forward your publisher card. If you attend that cong only a few times, they probably will soon forget what you even look like.
By doing this, you shouldn't need to actually move 2X. Because no one in your actual location Cong knows you, you should likely be able to disappear without looking over your shoulder.