Electronic – Why does the variable power supply have both a current limit and an overcurrent protection mode

Why don't you just invert your top diagram so it uses a P channel FET: -

This will mean a little modification to the current demand input - it has to be positive supply referenced.

You are talking a big boost ratio.

Orthodox thinking would suggest flyback BUT that means a transformer that you will probably have to wind/design yourself.

One way to handle big boost ratios is to use a diode pump on the end of a boost convertor. The diode pump approach is good for high frequencies and low currents which is where you are.

The number of stages in the diode pump can be your choice. More stages makes normal fixed frequency, hard switched current mode perform efficiently, but it uses more pcb realestate and raises component count and reduces the peak drain volts on the N channel switching FET, which makes a low on resistance device easier and cheaper.

OK go for 4 stages if you must use the chip out of the book. 2 stages would work on a S TRAP or other switching loss reduction scheme. A big advantage of the diode pump approach is that you can use a cheap SMD off the shelf coil.

If you need 90% efficiency at a normal operating frequency you will have to start dealing to switching losses. Current limit is intrinsic on any cycle by cycle scheme.

Speaking from experience the boost diode pump is much more efficient than flyback.