[BrianG]

Running a 1s lipo is probably the best lipo solution IMO. You really don't want to run a lipo down much past 3.5v anyway at such a low drain rate (less "bounce back" when load removed) so as long as you are still getting full output at LVC, then you should be good to go. I would make sure the Spektrum's voltage meter is accurate (by measuring with a meter and noting any difference) to ensure that what the display shows is really the state of the battery. I know on my Spektrum, the display reads around 0.3v lower than the actual battery voltage.

Running 2s lipo (or higher) with a BEC has been done (by MetalMan IIRC), the only downsides are 1) you don't know the true voltage state of the cells as they are masked by the BEC and 2) if the BEC fails, it could send full battery voltage possibly damaging the circuits. Although, since current drain is so low, it is less likely for the BEC to fry, but the chance is still there.

Another possible solution would be to use 2s LiFe and add a diode or two in series to bring down the voltage a little. 2s LiFe at peak (3.6v/cell) with a diode in series (dropping ~0.6v) would be 6.6v, which I know works fine. At LVC (3.0v/cell), the voltage would still be 5.3v. And this solution also lets you use the radio display to know the voltage so you can use the alarm.

I don't think overdischarging a Lipo at that low of a current draw will cause a Lipo to burst into flame; worst case is you have a dead cell. I don't think it would even puff since that is caused by overheating, and the radio doesn't draw enough current to do that. But like Ferret said, a BEC does draw current all the time, even when the radio is off, so you'd have to put it after the built-in switch, or add another switch.