While comtemplating what to do with the machine I stumbled upon this post:
It seems like this machine wasn't really optimally designed from the beginning. By adjusting the existing over-pressure valve I managed to get much better results from the machine.
But still those crummy mechanical bimetal thermostats were annoying me, and I needed some automation.
At first I used a couple of cheap industrial timers and a PID controller along with some solid-state relays to control the pump, grinder motor and heater, but they were clumsy and impractical so I decided to modify the machine for an external MCU-based controller.
I kept the solid-state relays, replaced the PID sensor with a LM35T and connected the appropriate wires to a D-Sub 9 connector on the front panel instead of the original switches.
After testing that everything was working using the connector, I was ready to move on to building the controller...