As you already know, a fairly stock MKV DSG, even running well, isn't worth much. Now you have one with a blown motor. More of a personal decision as to what to do. If you have a place where you could dismantle it and room to store parts you could part it out but that is a slow and cumbersome process and includes a lot of packing, boxing and shipping for dime on the dollar prices.
If you see those ads where they say they will take any car in trade, push it in or drive it in, go there and maybe get a new car this one is probably done. As it turns out I am in a similar boat and have a MKV DSG with blown trans. Hope it works out for you or you have a mechanically experienced friend that could help you put a used motor in it and get you back on the road.