Hello, I think I can help with your PCB assembly needs. Recently I have been working with a Shenzhen fab called PCBWin(www.pcbwin.com/a). My friend recommends this fab to me, so I had a try.
They said usually their customers provide the components to them, but they can also source the parts if thier customers need. Anyway, I choose to send them the components and let them make the boards and do the assembly for me. When I receive the goods they sent to me by DHL, I was surprised. After I tested the boards, the results are out of my expectation, because their work is just excellent! All the baords are good, no problem at all! So after this cooperation with PCBWin, I decided to work with them for a long time.
I hope my experience with this fab could do you some help. I am sure you will have the same good experience with PCBWin too!