There is *no* way to recover the data on a modern drive after a single wipe. It is actually impossible. It cannot be done.
The reason is simple - although you may be able to detect a tiny tiny bit of data from the previous recording, you've no idea how strongly overwritten it is. Now, with old drives which used simple on/off pulses to write data to the disk, it would be possible to see if the bit you're looking at is a little higher or lower than it should be, and infer the previous value from that. Modern drives use a system similar to QAM - quadrature amplitude modulation - to pack more bits of data into each transition on the disk. Since the signal is essentially analogue, you'd need to know how badly degraded the print-through was. You can't do this, so you can't recover data after it's been overwritten even once.
Well, you could just assume it's all been overwritten exactly once. I imagine that this would allow you to reconstruct a fair amount of data -- particularly if people take the advice in TFA seriously.
Back then a computer was $4000