If the feedback loop is TL431 based (TL431 is a 3-pin shunt regulator, aka Variable zener) you can change the resistor values to get 30V on the 12V rail. Formula for TL431 voltage is 2.5*(1+ (HIGH_SIDE_RESISTOR/LOW_SIDE_RESISTOR)) values are in Ohms and 2.5 is the TL431 internal reference voltage.
For example: 2.5*(1+(12000/1000)) = 32.5V
Note: It's advised not to go below 5K for the high side resistor or you risk damaging the TL431 with excess current.
Below is a typical TL431 application for optocoupler feedback:
**broken link removed**
When the output voltage reaches the TL431 voltage set by R1 and Rlower the TL431 becomes conductive, and since it's in series with the Optocoupler LED, when the rail voltage hits this set level the Opto LED turns on, which presumably tells the PWM or Oscillator circuitry on the other side to stop the PWM output or to alter the duty cycle, when the voltage drops below the set level the TL431 stops conducting and Opto LED turns off, PWM turns back on.
The current and voltage available with this hack is limited and depends highly on the secondary winding's inductance (turns) and current capability (wire gauge, grouped windings if any) but I have successfully hacked cheap cell-phone USB chargers converting the 5V to 12V for use with a router and even 19V for use with a laptop, albeit with major circuit changes (fuse, mosfet, current sense resistor, capacitors) but a well built 300W ATX supply primary and switching transistors should be more than ample and any bottleneck would be with secondary inductance and wire gauge.
Also, make sure you remove old capacitors and replace with 35-50V equivalents and make sure the rectifier for the 12V rail is capable of 30+ volts!