I guess I don't understand the purpose of using a faster op-amp. In the design, there are already 100 to 330 pF capacitors from output to negative that are already intended to reduce the loop bandwidth of the op-amp. The slew rate does not need to be that high if the loop bandwidth is not high enough to change the output voltage.
Secondly, there is a 47 uF capacitor on the output. So if there is an overcurrent, the voltage will not change until this capacitor is discharged. So that also slows things down as well. So it doesn't seem to me the op-amp type is really the limiting factor here. The original Practical Electronics design actually used LM741 which are even slower. I don't thing a power supply like this can react fast enough, for example, to be used as a laser diode power supply where nanoseconds of overcurrent blow up the device. So perhaps there's other changes that might need to be done first before the op-amp type matters?
Secondly, I thought since many dual op-amps have the same pinout as the LM358, it would be a safe choice as others could be swapped easily. I was thinking of the TL35072P which is available in DIP and goes to 44 V. But this is designed to be flexible so that if one wants to use it for a lower voltage then the LM358 voltage range should be adequate.
I could use an extra diode and filter cap for the op-amp supply. It's just that I figured that main capacitors are usually quite large (10000 uF+) and typically are going to discharge more slowly than say a 100 uF capacitor on the op-amps, but I guess this depends on the load. But I will consider this if it seems to be an issue.
I have attached many of the versions of the schematic I downloaded an examined from other forums before designing this one. This design has been worked on for at least sixteen years on forums as far as I can tell.
The circuit is still very close to the original. The LM358 used for the current limiting is rather slow. So it takes quite some time for the current limit to react. One such limit s due to the low slew rate: some 20 V / 0.3 V/ µs gives already some 7 µs of delay. Because of this the addition of the extra, fast current limit, like the mentioned VBE type version would be a good idea.
The are a few other possible improvements already known for this type of circuit:
One is using a separate filter cap for the OPs supply. This reduces the effect of the ripple at the main filter cap and can thus give higher output from a given transformer. The possible savings on the main filter caps is more than the extra diodes and extra filter cap for the OP(s).
The LM358 is also quite limited in the supply - there may be better choices, though not that many in THT case.