I thought the internals on the H2 I owned were pretty good, and I understand the H2n is better. I don't know how well it would work, but you could record four channel with it and put piano on one side and vocals on the other...
The new Olympus LS-100 might be worth a look too. I don't know anyone who has tried one yet, but Olympus claims it has the best internals in it's class and it has some other cool features a musician might appreciate.
I, too have a Sony PCM-M10. It has omni mics so if you did get one you would want to position it fairly near you, so it is getting your direct sound rather than room reverb. You'd want to put it in the best seat in the house, or the best spot in the room, where it will hear more or less like your ears (with a bit less stereo--though there is some--and a bit less bass).
Sorry to keep on you about this, but I feel it is pretty misleading to say that omnis "hear" like ears (even with the qualifiers). No less misleading than saying "cardioids hear more or less like your ears". Directionality for hearing is highly frequency dependent. The attached shows a polar plot for a (right) ear. It would be nicer if it had more frequencies plotted, but it gives a pretty good idea...Very different from either an omni or a cardioid, although maybe a little similar to a wide card. Also, ears have a steep roll-off at both the low and high ends (the omnis will get much more bass than your ears) and a pronounced "presence bump" in the range of most speech.
Really, the physiology of hearing is way more complicated than any mic I know off. Ears even have features like dynamic variable tension diaphragms (there is muscle that can increase eardrum tension, primarily to dampen sounds like chewing)...