I already heard back from the engineer.
Basically, there aren't any affordable improvements to make to this machine.
Here is his explanation
The run-away voltage "is probably due to the fact that your supply is unregulated and probably has a fairly high output impedance (i.e. as the load goes up, the voltage goes down - and visa versa). So, as your anodizing coat gets thicker, and also the resistive solution gets warmer its conductivity increases which reduces the load current on your power supply - and since the supply is not regulated, the voltage goes up."
He said that a capacitor would help my machines performance, but he said it would be expensive and difficult to find the one I need. We didn't discuss that any further and I didn't get a complete explanation.
He suggested means to make a cheap regulated variable power supply. Apparently there are cheap regulated variable power supplies available for around $5 but they only go up to 35 volts. He was calling them "317 chips". Now, 35 volts isn't very useful for anodizing so you would augment this with car batteries run in series. Car batteries are regulated. In this way you could make a regulated variable power supply that could go up as high as you want.
He confirmed that my multi-meter is set up correctly to measure voltage. I have a separate Amp-meter that is run is series, it's the little gauge on the black box. He said that my multi-meter may be damaged if I set it to read amps in it's current orientation. I'll be careful not to do that.