PWMing LED positive supply

I'm working on "dashboard" project that will have both LED backlighting and lots of LED indicators. I want to be able to brighten/dim everything in unison, much like a real car dashboard.

The idea I have in mind is to use TPIC6C595s to turn all the indicator LEDs on and off, and use a P-channel MOSFET to PWM the power supply that feeds both the indicators and the backlighting.

Since there are going to be lots of LEDs (several dozen for backlighting, several dozen more for indicators), there could be a few Amps being PWMed, passing through many feet of a "tree" of wires to reach all the individual LEDs scattered around a large panel. I'm worried that this could produce RFI, but I don't want to run scores of twisted-pair or shielded cables if I can avoid it.

I know that data drivers designed to keep long lines from turning into nastiness-broadcasting antennas use slow rise and fall times to reduce the amount of undesirable radiation. Rather than come up with a fancy high-powered driver, I'm thinking of doing a simple kluge: put 5 or 10uF of capacitance on the PWM line, which should increase the rise and fall times from scores of nanoseconds to a few microseconds. The waveform won't be a pretty symmetric trapezoid like the professional design, but I don't think that matters.

Has anyone tried doing something like this, and found that it solved an RFI problem? Did charging the capacitor cause some other problem (like significantly increasing the current when the FET turns on)?