The big grid is made up of four identical smaller grids ... since your clues fit them ok, then you may just have your answers in these four arranged in the wrong order. I steered clear of the full grid and instead drew up and completed the four small ones separately. Once that's done, you can physically shuffle them around (24 possible combinations?) and eventually you may just see some words which you recognise. Good luck, hope that's not too obscure!
What kind of normal person spends half a lifetime on the Listener as we all seem to do anyway? As you suspect though, a Roman would stand a better chance - but I somehow seemed to manage to recognise it ... maybe through luck, maybe because something Geoff Wood taught me actually stuck there for all these years (that's not another clue, he really was my teacher).