Rather than a voltage regulator have you considered an adjustable Buck Convertor? Both voltage and current are adjustable and remain as a stable output even when the the source input is unstable. We use these on Solar panels that are rated much more in voltage max than what the charge controller is rated to receive.
“Buck Convert-e-r”
Well, I know there are PWM buck-boost converters that can supply a constant voltage from a supply that may swing either above or below the target output (in this case, 13 volts.) They run significantly more money, of course, as they have to handle high current if Vin is low, and high voltage if Vin is high. However, I’m fairly sure these are made in big quantities for a limited input range, say, 8-18 volts (cutting out beyond either way) for automotive use. ??