Any suggestions would be greatly appreciated.
In an attempt to create a circuit that does circumvent most of the mentioned problems, here is my sketch.
Power source on the left will provide 12V, C1 is 0V on power up on '-' of LM311 , at the same time R1/D1 yields a positive voltage on + input on LM311, LM311 output hence will be 0V, which will make gate of FET Q1 0V, arming the fuse on startup.
Output voltage rises to almost input voltage, D1 dims, R3 charges C1, the voltage across Q1 will be the product of Q1 resistance (0.03 ohm for an IRF4905) and the current flowing through.
Too high a current through Q1 will trigger the LM311, the LM311 output will rise as it is pulled up by R2, this will close Q1 which increases the voltage across Q1, thus giving a foldback behaviour. D1 will light up signaling a blown fuse.
Closing S1 momentarily will discharge C1, pulling the - input of the LM311 low, the output of LM311 goes low, opening Q1 and thus resetting the fuse.
To increase the allowed current, a high value resistor (potentiometer) can be placed parallel to S1, making a voltage divider which decreases the voltage difference across Q1, also improving start up behaviour because it discharges C1.
Anything I've missed?