SVC-350 Power Supply Modification
You want to go with the transformer with the 18VACRMS rated secondary. 

A transformer with that rating will have a peak output of 18/0.7071 = 25.46V peak.

The rectifier diode will contribute about 1V of voltage drop to the 1000uF filter capacitors. So I would expect the filter caps to see a peak value of ~24.5V. 

During operation as the load is drawing power from the filter caps the voltage will discharge the caps by some amount less than the 24.5V peak. It is a very good guess that the average value of the voltage at the filter caps is the 22V as shown on the schematic. 

The beefy transistors that are inline with the current paths to the outputs are the linear regulator pass transistors. The TA7179 chip regulates the base current of these pass transistors to achieve the +/-15V outputs through variations in the load current.

I built a simulation of the transformer secondary and the diodes plus filter capacitors. Then I added a load resistor to each of the outputs. Here is the simulation circuit:



Note that the voltage sources have been specified at a sine wave peak of 25.46V. The two sources have been arranged to be 180 degrees out of phase as you would expect for a center tapped transformer. The load resistors were selected at 22 ohms to represent a nominal 1A load at 22 volts.

Here you can see the positive voltage at the filter capacitor and the current load into 22 ohms. Note the average value of the voltage is almost on 22V as labeled on your schematic.



In like manner this shows the corresponding negative filter capacitor voltage and the current load.