Ok, so after researching this a little more I'm confused. I found the fingering for what BGD said. I'll try it. Don't think I'll like the low E in it tho. But....
How can all 3 of these be the same chord? They come right off of our Chordie chart.
This is one of those rare occasions where I can actually contribute to a theory thread, so I'm on it.
The first chord (002013) is an INVERSION of Am7, but it's still an Am7. The low E sounds "off" because it's the bass but not the root. Another way to write it would be Am7/E. BGD is right; mute the low E and it will sound better.
The second chord (002213) is an inverted Am7 also.
The third chord (x02213) is not an inversion (just a straight Am7), but is tough to play unless your pinky is mutated, which mine is not.
As BGD said (again), unless you really need that high G to ring out, get your G from the open G string: x02010. Easy: Just an Am with a lifted ring finger.