Robin, very interested to see you having simliar issues to what I think I have.
When I bought my car I went to Stage 2 + Milly immediately and loved it, went on the RR day at Awesome and results were 252bhp/280ft-lbs which I was happy with, I have since added the fuel pump and has Stage2+ installed and a further RR day then saw 234bhp/275ft-lbs which was not all that great (wasnt a good day for K03 cars).
The problems I noticed was my boost would never meet requested, it would hit 1.3bar even if the ECU was requesting more, my gut feeling is that its a turbo issue or possible N75 but with the location of this on the TFSI being a right PITA its not easy to change.
I have had all the hoses checked, PCV swapped, DV swapped from forge to stock to latest revision stock which made no difference.
When I get the car back I will be doing some logging to see if I narrow it down further.
As for your original questions, you can get recon turbo's from VW, I had a recon K04 on my LCR when that lost its oil feed and creamed the turbo. As for which on the GTI - I would be tempted with a K04 - but for the price tag the KO3 would be the sensible option, like you say its powerful enough.
Do you have any logs from yours to see what its doing - boost / maf / n75 ?
Edit: just looked back at my logs from when I had the car first remapped and it didnt boost above 1.3bar back then but still made the first results above (in April)