The other night I was running Scarlet Armory and the tabard dropped, I won the roll but didn't have bag space so I would have to delete something, and run over to loot the body. But by the time I did that, the body despawned, I didn't get to loot it and the tabard wasn't mailed to me as lost loot, my ticket isn't being answered because I guess it's a high traffic time. Is there any way I can get my tabard back without worrying about speaking to a GM?
You won't get it back. GMs can not give you any items. Only items that you bought with coins can be restored. In all other cases there is no support for that and you will have to get the item again yourself.