Maybe the idea could still work if it focus on the remote-control aspect instead of memories and personality.
A remote presence system, enhanced with learning software to be able to imitate the reflexes and sometimes even actions of the person that controls them to delay the 'processing/signal delay'. Which leads to quite a few problems when some of the robots start to imitate more and more behavior, speech pattern and similar things. No full mind copy necessary, but the resulting behavior could be similar.
A remote presence system, enhanced with learning software to be able to imitate the reflexes and sometimes even actions of the person that controls them to delay the 'processing/signal delay'. Which leads to quite a few problems when some of the robots start to imitate more and more behavior, speech pattern and similar things. No full mind copy necessary, but the resulting behavior could be similar.