Yeah, that.
Adjustable compensation would be provided by adding a series resistor between U1 and U2 -in, and an R+C across U2, output to -in. Typical values would be 1-10k in series, and the R+C being on the order of 10k and 1nF. Actual values for best results could be wildly different, it depends.
Adjustment consists of reducing the value of C2 or eliminating it, and testing the output step load response. Increase or decrease the RC values as needed.
Step response: use a power resistor to draw an idle current about 10 to 50% of full rated load, then use another resistor plus a switch to draw a momentary additional current of 10-50%. The switch can be a MOSFET driven by a frequency generator so you get a constant sequence of steps. Read the output voltage with an oscilloscope, typically with AC coupled input, and in the 1-100us/div range.
It should be possible to obtain as good or better response compared to the 1000uF, without having to put the capacitor there. The benefit is not having obligatory energy storage directly at the output -- that is, if a short circuit occurs, the capacitor dumps all its charge (which can be a very destructive peak current of 100A+) before current limiting kicks in. With a smaller capacitor, less peak current is delivered, and the current limiting circuit acts more quickly.
Not that it's all that much energy (to the casual human, it looks like a little spark and a pop sound), but also not that a load will necessarily survive even with the current limit acting instantly (a 10A supply shorted into, say, a 2N3904, won't save the 2N3904 regardless of how gently those 10A are applied!). The advantage is seen when a few power transistors start to cook off in your amplifier or whatever, and instead of all of them failing in cascade (from the extra energy dumped from the capacitor), the damage is more limited (all transistors might end up dead anyway, but, survival is at least more likely).
Really, economically speaking, it's more a matter of how much time you spend replacing transistors when they die, times how often you need to replace them, versus the effort of improving the supply design. If your time is cheap and your parts are abundant, or your load is reliable (maybe because it already contains protections that this supply lacks), it might not be a priority.
There are other possible tweaks, say to improve recovery from current limit (it will take some time for the voltage to recover, and it will overshoot in the process), or to make the current limit adjustable, or to make it fold back to reduce power dissipation safely under fault conditions. These functions make a great bench supply, but are probably not needed for a simple power supply.
Tim