There should be formulas for calculating inrush current, if not, assuming you know the rise time, the inrush current will be (Load Capacitance * System Voltage ) / Rise-Time.
For example, system voltage of 40V, load capacitance of 3,000uF, Rise-Time of 100ms, inrush current will be
3,000uF * 40V / 100ms = 1.2A.
The purpose of the RC timing circuit is to limit this inrush current from the hundreds of Amperes to something more manageable such as a couple amperes or even less than an ampere. In this case, since the rise time is significant, the circuit just needs to not exceed the maximum power dissipation of the MOSFET, which in this case is 170W.
From the above example, the peak power dissipation will be 50W (40V * 1.2A).
It has a very low quiescent current, less than 1mA, something like the ZXTR2112F-7 provides a 12V supply without issue.
In order to implement automatic turnoff, bi-directional current sensing and some kind of timing element is required. This is most easily realized with a current sense amp and a microcontroller. It can be done using a current sense amp and window comparator with timing circuit, but that is really annoying to design.
Unfortunately all of the LTC700x series chips with current sensing only have unidirectional current sensing, not sure how it would behave with negative load current.
But, if the on-chip current sense amplifier recovers without a problem from negative saturation, then using the LTC7003 in tandem with a MCU can implement automatic turnoff.