Can I chime in?
First of all, OP, a word of advice: look for stereo microphones on whichever camera you end up getting. You say you want 1080p - what's the point pairing it with audio which sounds like it comes from a $1 microphone, recorded under water?
Second... unlike you, I have had NOTHING but good experiences with all my cameras running AA batteries (and that goes a long way back, to 2003, when I first got a HP210, then a Canon A310, then a Canon S3, then the Canon SX1). In my experience, two-three sets of good Eneloops or some reliable NiMH batteries(2700mAh and above) are just as reliable as a Li-Ion cell. In fact, I'm still miffed about the fact that my SX40 now uses proprietary stuff, instead of the tried-and-true AAs. It sounds like the Sony you mention had other issues...
You can probably guess by now that I'm a Canon fan, but I'm honest enough to admit that other brands can also make great products. In fact, my SO and I went looking for a camera a couple of years ago, and although I had been suggesting the SX200 (the precursor of the SX230 HS) at the beginning, we ended up agreeing that the comparably-priced Panasonic ZS7 was a much better camera.