My real question is why does my recording sound so far away? Why do the vocals sound too far back? I don't have a pre-amp yet...is that to blame? What can I do to make this sound better? Cleaner?
As ilduclo suggests, try getting closer to the sound source. Where were your mics relative to the stage and/or stacks?
The vocals sound as I'd expect through a PA.
I'm not familiar with your mics / battery box, but your levels seem okay, so a preamp may not be needed as long as the sound source is loud enough. I'm sure someone will chime in about whether the mics + battery box are sufficient for loud concert recording without brickwalling, distortion, etc.
Best thing you can do to make it sound better / cleaner is get your mics into a good position within the venue, where the sound seems to "float" all around you, rather than coming from a specific location / set of speakers. This is the "sweet spot", and it varies from venue to venue, night to night, etc.
Obnoxious crowd! When they're not blathering and screaming loudly, the music sounds pretty good.