I fear that this will never happen. In the best case scenario that I consider realistic, the TLAs will sense their impending doom well in advanced and will safely and quietly destroy all the data that might incriminate them of anything. This destruction might be punishable, but I think it is more likely that we will never even realize that it occurred.

The only way to take out a TLA and seize the incriminating data is swiftly and without warning. With warning times on the order of minutes, I don't think this is possible politically or otherwise.

The best we can hope for is to shut them down, and the best we can do afterwards is punish those responsible in absence of specific evidence against them (but I don't think that we have the guts necessary to do that. However as a real-world example of that sort of response, consider the show trial and execution of Nicolae Ceaușescu: http://en.wikipedia.org/wiki/Nicolae_Ceau%C8%99escu)