This sounds very similar to the ideas proposed at olsonb.com back in 2012 which are currently being updated in 2015 and discussed more.
Daniel Sheehan has studied Johnson Noise and determined it would not affect his devices significantly, so it is still open to debate as to whether eddy currents would immediately transfer back an equal amount of brownian motion. What if some of the radiation randomized in such a way that the heat never made it back into moving the magnet? How are we 100 percent certain, without actually doing the experiment? we can't just make assumptions, using circular reasoning, that the system will remain in equilibrium because the second law is always true. It could be that eddy currents get randomized, more than the magnet's motion itself, and not all the eddy current johnson noise pushes back on the magnet perfectly (what if the eddies are scattered and some of the magnetic field points elsewhere?)
Likely this idea of extracting energy from brownian motion will be falsified rather than verified, but it's worth experimenting and trying. The idea that a number of microscopic violations cannot become a macroscopic violation is on shaky grounds and is hand waving. How do we know? Where are the empirical studies? In order to remain falsifiable the second law has to be empirically tested. There may be limits to the second law (many have stated the second law is more of a general principle rather than an outright law: olsonb.com has a quote from Maxwell himself, at the top of the page)
See the following interesting proposals:
PDF: http://olsonb.com/articles/olson-brownian-interference-designs3-2015.pdf
Eddy current demon:
http://olsonb.com/images/olson-demon.PNG
For a gravity exploitation (geometry causes gravity to be switched off! virtually):
...see the milk-demon-2015.pdf on the site
But there are many more, that's just a few. This is uncharted territory, that is being charted via the olsonb project (plan b).
There are youtube videos listed on olsonb site which show nano magnets vibrating in distilled water. A strange paradox is that a bunch of nano magnets in high entropy disorder, will tend to clump together over time after random brownian motion - why are nano magnets becoming lower entropy over time, and not higher entropy? Entropy is a confusing subject. It still takes energy to break apart clumps of nano magnets and put them into a high entropy state (usually we consider it taking energy to put something into a low entropy state, but in the case of nano magnets, it takes energy to put them into a high entropy scattered state?)
Entropy and information theory is still not fully understood with many interesting paradoxes.