Thanks William.
Heathen is an interesting choice of word for ME (as is Eomer's repeated us of devilry). It is interest that in their earnestness not to leave Boromir lying like carrion, cremation is not raised as a possibility. Obviously there were no doubt good reasons why raising a great fire would not be the best idea but it is not even recognised as a possibility.
A final point to legate is that it was customary until very recently that the war dead were buried near where they fell. I say customary but the fact is that do do otherwise would have been impossible. The British only started repatriating their War dead in 1982 (within my memory) with the fallen of the Falklands War, and this was not automatic, but offered if the families wished it and not all accepted. While obviously there has been progess in transport and refrigeration the main issue is numbers. We lost 255 in the Falklands, a number which has yet to be matched I think by fatalities in both Gulf wars but nearly 20,000 in just one day at the Battle of the Somme. I suppose it is possible that Thranduil might have taken his dead back but I think Theoden, is the only case of of a body being repatriated, and he was a king - and it was possible to remove his body to the city immediately. His lords lie "under grass in Gondor". I think Eomer's eored buried their dead from the battle with the orcs at the scene, even in their own land.