I would start by dating the faunal remains using Carbon Dating. Provided the remains were the result of human hunting, this would provide a range of dates for when the midden was in use. Dating some of the charcoal would also work. Of course, we should look at the lowest layer of the mound if we want to see the oldest date of use, according to the Law of Superposition. The main risk is that the range for dates can be wide, which is why an average of the dates acquired is useful when dating a site.
The obsidian tools should also be analyzed to see what complex they match. If they match a style that has been previously dated, we can compare that age to the age of the faunal remains. Of course, this isn't exact dating. The dates for tool complexes rely on dating what is around the tools, not the tools themselves. However, if the faunal remains date differently than the complex, this would indicate that either the dates for the complex were incomplete or that something had happened to the midden to mix up different deposits.
The last method of dating I would use would be obsidian rind comparisons. As obsidian is exposed to the atmosphere, it grows a white rind. The thicker the rind, the longer it has been exposed. If one were to find a rind on a worked tool, this would indicate that the rind grew after the tool was formed. This is very imprecise, as rinds will grown differently in different atmospheres and can only be used to compare within a site. This would be a way to double check that the midden hadn't been mixed or stirred. If the thickest obsidian rinds are at the bottom, that means the Law of Superposition is intact. If not, this means we have a disturbed site.
