H4, Rode NTG-2 and a pocket full of batteries

Here's how I make the Zoom H4n work for me on a shoulder-mounted rig. The stereo shotgun mic bracket is attached to the front of the rig with a single large C-clamp, allowing me to mount it remotely from the camera when desired. I also have a self-powered long shotgun on a boom pole that works well plugged into the H4n's bottom mini-jack to bypass the built-in mics. The external battery for the H4n powers it for over 6 hours, available here:

Satechi iCel 5200 mAh USB Rechargeable Battery
http://www.amazon.com/gp/product/B001BF12QO

Outside a soundproofed studio, environmental noise almost always drowns out any preamp noise from the H4n. I run it in 4-channel mode supplying phantom power at 24-bit/48khz.

The P2 Tascam is nice. So is the R44
The Zoom products belong in the trash can.

I use Oktava, RODE and Sennheiser XLR mics and Tascam DR100 which I consider the absolute minimum for pro audio. Some of the units you've listed are way better.