A319LR maybe, but it's hardly going to be a major revenue generator
I could be wrong but I think thats what QR used when they started flying Doha-Berlin? I have certainly seen a QR 320 at TXL on a number of occasions. As you say not a huge revenue generator but if enough high yield traffic then a 319/320 would work for EDI. Or is it a question that EDI is too far on the edge of performanc limits to ensure a reliable and on time service without weather dependent tech stops needed?
I think QR use the 320 on a few of their East European routes like SOF and OTP, possibly ATH aswell but of course these are much closer in range than EDI.