This injects 187.5mV of hysteresis above the 3.00V shutdown to enable it.
You probably want 300mV of hysteresis above a shutdown of 11.5V with a drop of <100mV on the switch or < 100mOhms RdsOn. For precision any bandgap reference will do. Even 2V LED @1mA will do or a 1 cent silicon diode with 1mA at 600mV for a reference may do with a limited temp range.
What's more important? lowest cost or fewest parts?
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Not a common spec for 1 IC.
Generally protection is for OVP.
You could modify this
OVP OCP chip for UVP only using the Vctrl divided from 11.5 to 2.5 but then no hystereis. THen use the output to bias Ictrl to add hysteresis and not turn back on until Vin rises to 11.6 or some level that does not cause motorboating on/off.
Then use a suitable Pch MOSFET.