Second Reflow with BGA
It would probably be better to use a hot air rework station to replace the BGA. You still have to be careful with components with this method, but it can be done. I would find a service to do this for you.

If not, then even if the other components move around (which they shouldn't move too much because the solder has surface tension that keeps the part in place), you should be able to fix any problems with a hot air rework gun (and flux) or two soldering irons for passives. 

No matter what you do its going to be expensive, BGA's are hard to deal with and the process have to be done right because you can't see the connections unless you have an x-ray machine.