You're correct in identifying dynamic range as one of the major issues here. An A2D with an extremely high number of bits would help, as you could recognize both the faint and large signals simultaneously, and with prior knowledge of the large transmitted signal it could be removed from the data.
But there is another issue, which is the dynamic range of the RF hardware itself. Their experiments were conducted at 0dBm (1mW) transmit power, but that is not at all realistic if you want to get decent range, a more realistic power for longer range would be 10-100mW. With 20dB (factor of 100) cancellation there is then up to 1mW heading in to the receiver, which is way way too much for typical RF CMOS, and even for typical SiGe receiver chips, the output will be completely garbled by distortion at that high power. In fact the chip they're using to do the analog cancellation (QHX220) can only take 4 microwatts in at 2.4GHz before it is completely distorting. They probably want an IIP3 (a measure of dynamic range) of minimum 10mW to limit the distortion, which is fairly large for typical receiver hardware. It's not terribly hard to do with GaAs chips (but more expensive) and it will take some work to do it in CMOS/SiGe which is cheaper.
In other words they tested under very specific conditions, and currently there needs to be additional work done on the RF hardware end to make this viable in an actual product. Not that I'm criticizing them of course, their interest is exploring more the communication aspect. If a company wants to make a product of this all it takes is money to fix the RF dynamic range issue, they're not pushing the limits of possibility yet.