I have recently changed my address (was required to move back home) and am in the middle of hearing back from LLM programs. Would it be prudent to wait for the email admission and then let the school know to send the materials or should I send off the change of address now? My concern is that the admissions officers are busy so I would rather wait...

I would recommend wait until you receive an admission offer. As far as I know, the US universities only mail you the package after you get admitted. So no need to let them know the address change before that.