Hi earckens,
Yes, the leakage current data on the 1N4148 data sheet it is confusing.
One thing to know is that the reverse leakage of a diode is proportional to the reverse voltage.
Also, when you power supply is operating in the normal voltage stabilization mode (not in the current limit mode) the voltage at the LM723 pin 4 is constant at 6V nominal. That means that the reverse voltage across the diode is always 6V, so you need to look at the leakage current for 10V reverse voltage on the data sheet, rather than the reverse leakage current at the maximum safe reverse voltage of 75V for the 1N4148.
Another point is that a particular version of an 1N4148 is liable to have a reverse leakage current close to average rather than maximum, while a Schottky diode, being leaky by nature, is more liable to have a leakage current higher than average (I know that mathematically that is garbage, but that is what I have found and I have messed a lot with both types of diode).
spec
PS: I could not find any data on the 1N60; do you have a link to the 1N60 datasheet?