You should be able to route a 1 mm bga with PCB123. You will need to allow your via to share some space with the bga pad as shown in the image below.
Use the smallest hole size .014" with the smallest via pad size .025" (only available when a multi-layer board is selected) and you should be able to route using7 miltrace with a 6 mil space. You can order this directly through PCB123. This will only work if your bga pads are about .5 mm diameter. If you would like your file reviewed you can either attach it to this thread or send your file to email@example.com