Cleaning this would be easy if the thief knew what he was doing.
Break the sum into several thousand random size wallets and simaltaneously start a massive hoping trail across various alts and exchanges via a few herds. I would love to see these "heroes" track tens of thousands of smaller wallets converted between dozens of alts, re assembled and mixed again. Estimated loss is 20% of the haul but $180 Million cleaned still isn't too bad.
~BCX~
The problem with cleaning so much money is that it just takes 1 Satoshi to bring things back to him, just 1.
And something further to consider is the laundering itself is going to leave a huge fingerprint moving so much around.
Perhaps a fair analogy is how the NSA can still track people who are using TOR because, in part, of TOR's latency. There is a similar, but much clearer fingerprint the thief is leaving as he moves coins around, cleaning or not. The depths at which Computer Forensics is capable of is mind blowing and then throw some big computers into the equation.
A bigger fear is that these intelligence agencies get their hands on the coins and don't tell us...