My solution is similar to your resistor, though used a PWM fan control module that I ran direct from the DC power switch on the rear of the case to the controller, ensured that there was a good ground, and installed toroids on the in and out of the controller. Did not totally eliminate the noise, but could dial back the fan to reasonable audio levels that also had low RF interference.
Not perfect, but did reduce to tolerable levels. It also allows me to adjust the fan speed based on conditions.
Best is always fanless for low noise of all types. An aluminum block on the back of the case with the fans mounted to the block would be the best in my humble opinion.