I favor the "bounce" method.
Move far away. Have your cards sent to a new congregation, preferably across town. Wait until announced in this new hall. Then, tell them that as you are new and still settling in, you will be moving to a different apartment in another territory. Cards get sent to another congregation and then you disappear.
You "bounced" your cards off a congregation that doesn't know you, into another that doesn't know you -their final resting place.
Even if they call your previous congregation, it is just the "bounce" congregation! They couldn't pick you out of a crowd.