I don't have such difficulty in imagining Orcs singing. We do tend to associate singing with beauty, but singing serves many purposes. Rugby players (not that I am equating them with Orcs!
) are well known for getting thoroughly drunk and singing crude and colourful songs. There is also the Haka (sp?) chant - as seen performed by the All Blacks before a match; this is said to derive from ancient Maori war chants. Armies sing as they march to war, and a lot of our popular music is incredibly brutal and visceral. The urge to sing, I'd say, occurs to all sorts of people and in all sorts of situations!
If these Goblins are indeed Orcs, then it interests me that they seem to have some independence and have developed their own realm. But then I remember in LotR Gorbag and Shagrat discuss possible 'retirement', so maybe lifelong (eternal?) service to whichever Dark Lord is currently holding half of Middle-earth in his thrall is not necessarily a given thing for Orcs?