If the Paddle was simply a neutron would it radiate? Not sure if it could have a temperature but it would certainly accelerate during the process. I may have asked you this before but have forgotten. I think the answer was yes, due to its positive and negative parts even though it is neutral, somewhat similarly to an atom.
The only refutation of the Demon (beyond the obvious you have stated) that I have heard is a quantum one with regard to the Demon's uncertainties in the knowledge of the particles and the gate (now paddle in this case)
One other point is that classically if you could start out with some part of a system at absolute zero it would not remain that way very long, the system would move to a different state. Since classical mechanics is reversible, this should prove (assuming classical mechanics) that absolute zero could be achieved. The "different state" could move to the original in theory, no matter how unlikely.