This morning I went down to the garage and pulled the front off of the control box to begin troubleshooting the problems from yesterday's testing.
The first thing I changed was to move the leads that the Elements On lamp connects to. These were connected to the Power-In terminal on one SSR and to the Power-Out terminal on the other SSR. This is why it was lit continuously. I moved the leads to the same terminals that the heating elements connect to. Now the lamp should only light when the heating elements have power.
Next, I had to figure out why the heating elements were not getting power. I looked at the screw terminal diagram on the side of the PID controller and I noticed that there was an empty screw terminal between the two lines to the SSR. I unscrewed one of the connectors and moved it over one screw and tightened it back up.
I plugged the controls in and turned it on and . . . . NOTHING. The elements were still not heating. This time I opened the control box and left the front panel hanging while I started it up. The SSRs have a small red LED that indicates when they are energized. I wanted to see if they were even trying to close.
Then I noticed that the control (or input) side of the SSRs are marked (+) positive and (-) negative. The control side of the SSR is a DC circuit. I wondered if the screw terminals on the PID controller had polarity too. Sure enough they do!
I unscrewed both SSR control terminals and switched their positions. I tightened these down again and closed the works up.
This time everything worked as intended!
I entered a setpoint of 300 °C and let it begin heating up with two bricks over the top of the heating chamber. The temperature steadily rose and as it approached 300 ° the heating elements were turned off, but there was an overshoot of 68 °C. Then the temperature slowly came back down to 300 °C where the controller maintained it within 1° or 2°.
Next I loaded a crucible with clean aluminum scrap and set it in the heating chamber. I changed the setpoint to 700 °C and covered the heating chamber up. It took about an hour, and this time the temperature rose up to 700 °C and it did not overshoot. The aluminum that I charged into the crucible melted! I scraped off the dross and poured two small ingots from my first melt.

While this test was running, using the infrared non-contact thermometer, I checked the shell temperature, the heating chamber firebrick temps, control box temperatures (especially the temps at the heat sinks on the back), and everything was about what was expected. The firebricks covering the heating chamber were about 250 °C, the back of the heating chamber bricks were about 160 °C, the furnace shell was about 36 °C to 40 °C, and the heat sinks on the back of the control box did not rise above 40 °C.
I expect that the shell temperature will come down once I have installed the ceramic wool insulation. This will cut down on convection and radiation from the heating chamber to the steel shell.
Tomorrow I will begin working on the lid assembly.