Keep in mind that an RC filter is NOT a brick wall filter. If you look at a plot of it, there will be a gentle slope off of the frequency.
Just did a quick check...http://en.wikipedia.org/wiki/RC_filter
About 2/3 down the page they show the "step-response" graphs.
I'll reiterate what others have mentioned and add a little more.
* Since RC filters have a gentle slope... higher sampling rates will shift their DAC noise up in frequency and make the RC filters more effective. This is often called "oversampling" in the CD/DAC audio world. This won't help with RF noise, though.
* Motors are extremely noisy devices in the RF realm. The closer they are to an amp/signal wire, the more electrical noise there will be on the output. Shielding the motor will help a little but is usually more trouble than it's worth.
* Grounding and ground loops can be a royal PITA to clean up and fix. The simplest way is to use a star ground for everything, but this isn't always practical. If you're using a ground bus, put the high current and noisy stuff closest to the PSU ground. Digital stuff is just after that. Analog output is usually furthest away. Remember V=IR? Ground returns have a tiny resistance and high current pulses will show up as a voltage somewhere. If that somewhere is a sensitive amp, it will translate as noise into the output device.
* As a side warning, just about any side by side combination of resistor and capacitor will try to form some kind of pass filter. If you try stacking these, you will end up with a complex filter. I think this point is mostly irrelevant with an AVR+piezo, but it's worth mentioning for the archive.
* You can try adding PSU filter capacitors at strategic places, but make sure they are grounded properly (star ground preferred). See my grounding paragraph above.
* You can try adding filter inductors at strategic places, but do not use them in series with high current devices. I generally don't like inductors because they can become a short range antenna for the noise.
Just about everything on this list comes from what I've learned lurking on the audio forums. Didn't think I'd be using that knowledge here.
There are more complicated setups and explanations, but I think some combination of the above will help you. It's late and my eyes are crossing, but I think I hit on the major points of your problem. Good luck.