Ok for those of you following along at home. I went to Jaycar and purchased a 4.7nF and a 1nF capacitor to do more testing on my strat pickups.
After testing them here is the actual capacitance:
4.7nF = 3.96nF
1 nF = 0.977nF
As you can see the 4.7nF isn't even close but that doesn't matter in this application because I just need to know the actual capacitance to do the math.
I tested the middle pickup again with all four cap values.
0.687nF - 3.6H
0.977nF - 3.42H
3.96nF - 3.56H
10.5nF - 2.63H
It's quite clear that the largest cap for some reason is giving an outlier. The other 3 results are fairly consistent and give an average of 3.53H. I need to do some more research as to why the largest cap is giving a bizarre result but these results rule out my initial hypothesis relating to the stray capacitance of the pickup.
Next step is testing self-inductance of the capacitors to see if that is what is causing the issue.