What impedance should I get when testing a volume control?
The purpose of the control is to present the correct impedance to your amplifier based on the number of connected speaker pairs while providing a local volume control for each pair of speakers. 

Without the controls, paralleling multiple speakers would reduce the impedance by a factor equal to the number of speakers. For instance, four 8 ohm speakers connected in parallel would normally appear as a 2 ohm load to the amplifier. But the controller effectively multiplies the impedance of each speaker so that when they are connected in parallel, they present the correct impedance to the amp. So the 8 ohm speakers in the prior example would have their impedance multiplied times four. Now when four 32 ohm speakers are connected in parallel, their combined impedance is 8 ohms.

The impedance multiplication is simply selecting different taps on a transformer. Measuring resistance of a transformer winding is not a direct indication of impedance.

To troubleshoot this system, here are some steps I would recommend. Don't overlook the possibility there could be multiple problems.

Check that all controllers are configured to multiply their load by eight.

Disconnect the wires that run from each control back to the amplifier. Measure and compare the resistance of each controller where the wires were connected. Any substantial difference in resistance should be investigated further.

Hook a signal source to the still disconnected controller and audibly confirm that the local speaker pairs are functioning and the controller volume control works. Repeat this for all controllers.

Then with the wiring still disconnected from the controllers and from the amp, take resistance measurements between all combinations of the four wires. This should show infinity (an open). Then check each wire for a short to AC ground. This should also show infinity. If the pairs daisy chain from one controller to another, you should repeat these measurements for each segment.

If none of this has turned up any problems, then connect the amp to the house wiring and add and test one controller at a time using a low volume setting on the amp. When the fuse blows, you have a controller and its wiring to further investigate. Remove that controller and continue adding others.