My last 2 rentals registering the TM30 was on my list of requirements for the agent. Eqch tome in Pattaya and Chiang Mai they have done this. In CM it needs to be completed again after travel. I fly back in today from Vietnam. The agent asked me yesterday to tell her when I am back and she will update the TM30.
Someone posted about doing the extension in Phuket a few weeks ago. It was quite a detailed post. Have a search. Basically yes, all original documentation. Employment letter updated too.