AA battery powered mp3 player?

There may be another alternative; portable audio recorders.  The professional grade recorders generally have excellent playback quality and all the ones I’ve seen run on AA or AAA batteries.  The Yamaha C24 meets most of your requirements.  It runs for 34 hours on one AAA battery, accepts micro sdhc cards, has a low-power backlit monochrome screen, and some sort of clip (although I don’t think it’s what you’re looking for).  They aren’t designed for the purpose, so they don’t have FM tuners, generally don’t accept a wide variety of formats (usually just wav and mp3) and tend to be rather expensive, but they seem to be the closest things on the market to the long sought-after AA/AAA powered, removable storage mp3 player.