You have 8 sensors, but you only need 3. There are 56 unique combinations of 3 from 8. so you run the 3-input equation 56 times and take the average. A fair strategy for dealing with an over-defined problem. I do something similar. But these 56 values are not independent. Most of them are dependent on each other. You can't get something from nothing, you still only have 8 unique numbers to start with.
Here's an analogy. Flip a coin, and it comes up heads. That's one measurement. The other side is tails. Measuring the other side provides no value. It's determined by the first. Two sided coin, one degree of freedom.
If you have two coins, then you have two degrees of freedom, requiring two measurements. Not four. And so on.
There's no question that closed targets can be more accurate then open. But it's certainly not because 56 is bigger than 12, 8, or 4. It's because closed targets do not have to deal with physical movement. Which can be handled through frame construction and stability. The precision of the internal calculations is not important.