I agree this approach is logical, but it will require "calibration" to define the output desired from a given input. Lots of experiments and work to avoid a modest cost.
This should do the trick. It's fleshing out the ideas suggested above.
R1C1 integrate the incoming PWM to give a voltage 'msi' proportional to the mark/space ratio. The 555 is triggered by the input PWM and generates pulses of width controlled by the voltage 'cv' on pin 5. The 555 output is integrated by the pot and C3 to give a voltage proportional to the output mark/space ratio. A fraction of this, 'mso', is fed with 'msi' to the comparator. The comparator output is smoothed by R6C4 to give 'cv'. By virtue of the pot the output m/s ratio is kept a fixed fraction above the input m/s ratio.
R8C5 are chosen to suit the input PWM frequency. Online search indicates this is ~24kHz for the PS3 fans. If the output pulse width exceeds the input pulse width the 555 will not be triggered on each cycle: nevertheless the long term average output m/s ratio will still be controlled in the required way.
It might be easiest to just drop the 555 timer. and use a microcontroller, the microcontroller just needs to sample the input pulse and period and output a pwm scaled by a multiplier. I'm not very familiar with other companies offerings )atmel or ti...) but I know microchip has peripherals for just such a thing, using an input compare you can determine the period and duty cycle, multiply it by a factor you want and use the pwm peripherals output. the chip shouldn't cost more than a dollar or two, or free if you ask them nicely. embedded programming has a bit of learning curve to it but if your familiar with c programming it shouldn't be too hard to pick up.