I was also playing a bit with ATX PSUs to serve as battery charger, and had successfully upped the voltage by modifying resistor values.
But you want CC and CV, and you cannot achieve that without some more circuitry.
I think that best thing to do is up the voltage to whatever you need and then use a LM317 for variable voltage and another one for constant current.
If you aren't sure how to change the output voltage this schematic in attachment will help you out.
Look at the resistor connected as voltage dividers to the pin 1 on KA7500 (R33, R34, R76).
Note that aren't all PSUs the same, so values may be different.
Add for example a 100k variable resistor (pot with only 2 pins hooked up) in series with one of resistors (R34) and hook up a voltmeter to the 12V output (also 5V, and 3.3V will increase) and turn the pot, and you'll notice how the voltage increases.
At some point everything will turn off (don't worry, you didn't burn anything) it's the over voltage protection doing its thing.
Look at the A2.1 op amp, that its job, to send signal to KA7500 when to turn off to pin 13.
You will have to disable or adjust the that op-amp (easiest thing to do is to desolder pin 13 and isolate it, cut it or whatever if you aren't going to use it).
And that's about it. If you need help, ask.