Honestly there's enough tuning potential in the 1.8 that you're far better off doing a turbo swap then replacing the whole drivetrain. Though if you realllly want to, your best bet is the 2.0 out of the Mk6 GLI, which lacks the exhaust timing that is found on the GTI, can work with the 1.8 ECU as a drop in. Still, you're better off getting an Is20, you can find good low mileage examples from GTI owners, and it's a relatively straightforward upgrade to horsepower in the high 200's on pump gas.
Out of everything you said, my biggest concern would quite frankly be getting a DSG to play nice with an Aisin/5-spd ECU. Don't doubt that it can be done, just know that it's uncharted waters you're heading into if you go down that path.