Yes, this is exactly the sort of example I was looking for! Do you have any further details? Maybe I should work it out myself, to see if our results match up.
I suspect that there are all sorts of examples like this, accessible in theory and models of measurement in experiment, where things basically match up with with Born probabilities. Though I expect in some degenerate case they won't, just as, as the fluctuation theorem in nonequilibrium shows us, sometimes the second law is inaccurate, because whatever we call 'entropy' decreases.
I suspect that there are all sorts of examples like this, accessible in theory and models of measurement in experiment, where things basically match up with with Born probabilities. Though I expect in some degenerate case they won't, just as, as the fluctuation theorem in nonequilibrium shows us, sometimes the second law is inaccurate, because whatever we call 'entropy' decreases.