If you want it that high, I would suggest using wok seasoning methods instead of cast iron. Basically, you “blue” the pan (develop a black iron oxide layer) by holding it at 550F for an hour or so. You’ll burn off the oil every time you use it, but the black oxide layer is relatively non-stick. This will work better with carbon steel than cast iron.
Alternatively, you might consider an even heavier pan, to hold a 400-450F temperature even longer.
The burner will get well over a thousand. Without something cooling it off, a pan can overheat even on low.
If you want it that high, I would suggest using wok seasoning methods instead of cast iron. Basically, you “blue” the pan (develop a black iron oxide layer) by holding it at 550F for an hour or so. You’ll burn off the oil every time you use it, but the black oxide layer is relatively non-stick. This will work better with carbon steel than cast iron.
Alternatively, you might consider an even heavier pan, to hold a 400-450F temperature even longer.
The burner will get well over a thousand. Without something cooling it off, a pan can overheat even on low.