The PID would definitely help over temperature when the pot gets low. My Lyman 20 lb. pot had the bi-metal thermostat external to the pot. So the "on-off" of the heating element was controlled by the air temperature of the "housing" where the thermostat was mounted.
The PID gets the lead temperature via the thermocouple that is immersed in the molten lead. The PID can control temperatures by + or- 10 degrees.
I switched to the PID after three rebuilds of the wiring and terminals of the factory set-up. The next rebuild would have required the thermostat replacement. I was going to have $40. in the rebuild and could get the PID for $80. I went with the PID and my casting is a lot better.
I never had a thermometer so I was just "in the dark". With time the setting of the thermostat needed to be set higher and higher til it finally died. I also had no idea when the lead was back up to temp. after adding ingots.
I recommend the PID. Also get a hot plate to pre-heat your molds.