At this point, I'm looking at an Arduino Pro Mini running on an 8 Mhz external resonator. While it has a 3.3V regulator, the schematic suggests that can be completely un-jumpered. The Mini would then be powered directly by a single 18650. I would probably not build in a charger, but just replace the discharged 18650 with a charged one as needed.
There are Arduino libraries for both IR remote and keypads, so the programming should be pretty easy. I don't have a demodulating IR receiver, but was able to get the Roku IR codes for Back, Left, Right and OK using my scope and a plain IR phototransistor. For those interested, the Roku format is 32-bit NEC.
So any of the three column lines would interrupt the Atmel and wake it up from deep sleep. On waking up, the sketch would identify the current key being pressed, wait for it to be released, then look for another keypress for perhaps a second. If another keypress is found, the first key value would be muliplied by 10, and second key value added in, then wait again for release. When a timeout finally occurs, the accumulated channel number value would be looked up in a table, and its corresponding My Channels position would be compared to the current position, and the number of Left's or Right's needed to get to the new channel calculated.
After all the moving is done, the processor is put to sleep.
The big problem is probably going to be finding an appropriate box to put it in. There ought to be a law that says anyone who manufactures a keypad has to specify a project box that fits it. :-) Or maybe there's a box that comes with a keypad installed.
The IR library controls the duty cycle of the transmitter, and I believe it's 50%. But the recommended value is 25-33%. 25% would in theory save half your power usage unless it also effectively cuts the range in half, which I assume it does (otherwise this would be a free lunch, which is not permitted).