Oops - I should have said 16Mhz (not sure where I got 20 from, but it's definitely 16).
Right now, whilst trying to get this thing down to sleep, I've literally only got the chip on the board. I want to connect a touch screen (eg. a Nintendo DS screen), which requires 2 analogue pins and 2 digital. The RF module takes one data pin, although I've found it can be powered by an arduino digital pin (so I can control the power consumption of it). I'll see if I can knock up a diagram or something...
Having hacked about with this a bit more, I'm starting to wonder if I need a physical button to wake up the remote, and then use the touch screen. That's absolutely not the design I want, so maybe I'll look at some other interrupt source (tilt switch?). All of this isn't really where I want to go though - I'd prefer to find a way of stripping the atmega chip down to the bare bones so that it draws <10mA while idle (I'm not too worried what it draws when you're using it). To get that far, I'm going to need to work out some way keep the chip in sleep mode (as deep as possible), but with occasional (eg. every 500ms) interrupts to see if you've touched the screen.
Any idea what difference dropping to 8Mhz might make? Maybe I could use the internal oscillator and save a few components too...?