I can imagine the energy for the second neutron could be "borrowed", and there would be a period where there would be no neutron. The energy pumped into the system would be the "interest" on the "loan".

But then how would he know that he was observing the same neutron at an earlier time. He might be able to tell he had duplicated the earlier "state", but how could he tell it was an earlier "time".

As you point out, I don't know of a measurement which can distinguish between neutrons, just characteristics of neutrons which can be imparted to them.

Boggles my mind, but then the statement about "hoping" to have a "working mockup" and starting experiments in the Fall seems marginal, anyway.

I'd like to see it work, though.