The original circuit does not work. The transformer's voltages are too low.
The 18V center-tapped transformer has peak voltages of plus and minus 12.7V. The rectifier drops it to 12V and the ripple in the main filter capacitor drops it to only 11V at a 1A load. Then the 12V regulators and your 15V regulators will not work.
The 12V regulators need an input of at least 14.5V and your 15V regulators need an input of at least 17.5V.
Sigh. Every project from this author is wrong.
You need a 28V or 30V center-tapped transformer for your 15V regulators to have enough input voltage.
