Honestly, I think it'd be way cooler if you did a FI swapped drive-train from a salvaged Passat/CC 3.6 4mo. I've seen them both in salvage auction selling well below $5k. 2nd and 4th gen haldex respectively a base of ~300hp in a fairly light compact box thats already set up to fit..mostly. Then TT it up. RAI was looking for 600+ hp out of their project 3.6 CC. It would sound way cooler than a LSX, it would be AWD like you wanted, and VW kids wouldn't hate on you so much.
Even doing all the work himself, this would still likely reach $10K-$15K in parts and materials before he is all done.
Anyway going back to AWD if you find salvaged parts and can perform the work yourself it should end up being what a base R would cost including what you've already paid for the GTI. Now if you want to be a true badass you'll shove an Audi 4.2 under the hood or even a new 3.0 supercharged, then you sir would have the most awesome mk6 GTI ever.
I have nothing to add, save for the new-found knowledge that there is slang for huffing the fumes from excrement.
This is like synthetic cannabis meets two girls/one cup.
Bravo.
OP:
The MKV GTI/R32 swap mentioned earlier was being done entirely by the owner. He/she had all the necessary skills in welding, fabrication, etc and did all the work in the garage. The issues they ran into were basically that you will need the floor, gas tank, entire drivetrain, and entire electrical system (you need most of it so might as well be all) in order to control the AWD. IIRC they could successfully install the hardware, but they couldn't afford the supporting systems necessary to actually make it work.
Since the Golf R is not here yet, you might be able to source a MKV and retrofit the systems, or as mentioned try a CC. But buying new this will cost you more than a Stage III Golf R would and it would still have less power.