If your end goal is getting the data back, a new motherboard will not help you because the motherboard is the component where all the data is stored. So if you replace it, you'll only have the data that was on that board.
They said you need to "motherboard reball stencils?" I'm trying to figure out what they may have meant by that. Perhaps they didn't have the correct stencil for the job, or they needed components they couldn't find? Did they tell you exactly what the problem was?