Hi,
From my experience, CCFL driver boards rarely use a simple voltage to control the brightness of the tube on its output...its usually PWM, even on 'generic' boards. Running the 12v driver board at a lower voltage, it might not be able to reach the CCFL's start voltage, and if it does, the output probably wouldn't be linear to your control voltage.
However, if I understand your problem correctly....you have a control 'voltage' that is inversely related to the 'brightness'...so 0v = 100%, 5v = 0%, 70% = 1.5v? correct? And, you wish to control the driver boards power supply using this control voltage. Hmm, a LM317 might actually be able to do this. However, there are many here who are far more versed in 317 designs (Hero999, RonH?), I fear I would be out of my depth.
The reason I'm posting is I just don't think varying the driver boards power is a good way change the CCFL's brightness, almost all inverters I've seen have a 'control' pin. This is usually PWM, but not always, sometimes it uses a voltage as a reference, which will not draw much power at all, and can be controlled by an opamp circuit effectively.
If it does happen to have PWM control, a simple sawtooth (or traingle) wave generator and a comparator should do it. Seeing as how your control voltage is inverse to the output, you would simply swap the inputs to the comparator.
If it doesn't, then I'm out of idea's
You could always check ebay for ccfl driver boards for your monitor..theres loads on there.