Your Fluke tester is probably the problem here. The
manual lists only a 2 kΩ input impedance for DC (see screenshot). This is a really low value. Almost all modern testing equipment has an input impedance in the 10 MΩ range, even the very cheap Chinese stuff.
I don't know the specifics of your battery boxes, but they will most likely connect the positive battery terminal to your mics through a resistor. This resistor forms a voltage divider together with your Fluke tester's input impedance. And since the input impedance is only 2 kΩ, the Fluke tester does not "see" the full voltage. My guess is that the internal resistor in your battery box is somewhere in the 2.2 kΩ range. Given a 9V battery, the voltage divider would result in a 9V * 2 kΩ / (2 kΩ + 2.2 kΩ) = 4.3 V measurement. That looks to correlate with your real-world measurement. Throw any cheap modern testing equipment at it with a 10 MΩ input impedance and that measurement becomes 9V * 10 MΩ / (10 MΩ + 2.2 kΩ) = 8.998... V (rounded to 9V).
The good news is that this also means your battery box is probably outputting the full 9V from the battery.
Just get rid of the old Fluke. It's no good, except for measuring a battery's open circuit voltage (and a few other things).