Their conclusion in the OP was AIUI that _many_ stars produce novae serially. So we should surely be able to match series of novae (along a stars trajectory).

Their conclusion in the OP was AIUI that _many_ stars produce novae serially. So we should surely be able to match series of novae (along a stars trajectory). The time between classical nova outbursts is estimated to be on the order of 10,000 years, so the previous outburst of this particular nova was probably long before the development of writing. In addition, it likely takes only a couple of thousand years for the expanding shell of gas to fade from visibility, so it's probably not possible to find the traces of previous outbursts along the trajectory (although that would be cool).