XRF is very accurate, but will only tell you what's in the surface (about top 5=10 nm or so). For bulk composition, I would dissolve the sample in acid and run an ICP-MS or ICP-AES on it. Flame AA is also good (but somewhat dated).
Galbraith Labs in Knoxville, TN does a lot of analytical testing. We've worked with them in the past and they are good, and turnaround is prompt.
Galbraith doesn't list prices on their website but whatever it is, I can't afford it. So I guess this is the end of the road for my quest to figure out what makes this batch of reclaimed shot special.