Thank you, Gentlemen! You're responses are fantastic! Complete with QRH and FCOM references! So what the instructor told me was spot on after all.
In my continued quest for fuel savings I will now experiment in continuing at cruise beyond the TOD but not so far that I'll have too much energy approaching final, pull for real thrust idle until the magenta profile doughnut centers up, hopefully very close to final, and simply push for managed descent so I don't end up level in thick air for long.
But does anyone know that I'm wrong in thinking that real thrust idle may indeed be additional drag, akin to props not feathered? If I discover that that is the case, I will immediately stop attempting to save fuel by using open descent from TOD..