The turnaround time you requested is going to be really tough.
Last time I ordered a custom suit in Japan, it took 2 weeks from initial consultation to final fitting and that was a "rush" job. After saying that, it was the best fitting suit I had ever owned.
If you go to Shanghai, you can get a custom suit in 3 days delivered to your hotel room and it is inexpensive. While the quality of the cloth and the stitching to be, at the onset, without problems. My suits just don't seem to last as long as my Japanese custom suits.
Given that I need to also order a new suit soon, probably will have it made in Japan again.