My original thought was that the stove controls that I have been in contact with over my lifetime are basically just that: on or off. I realize that I have probably run in an incredible string of bad luck (AKA cheap stoves), but I have yet to find one that will "tone down" to where things keep receiving heat without them boiling or frying. This applies to both electric stoves and gas stoves (which always turn off the flame long before reaching the "off" point, but not at any definitely delineated point along the way). Both my ineptitude around a stove and the first of my three signature lines must be kept in mind when considering this issue.
The gas stove valves with which I'm familiar have their lowest "on setting" farthest away from the off setting. They start with off, then twist to high, and more twisting lowers the flame. When they reach the stop, the flame is very low. When they're set up this way you can quickly twist the knob to a very low setting without any danger of putting the fire out.
It seems like you've been fighting the system.
