So I think that I FINALLY got a working unit. I am not joking, this is unit number 6!
I shouldn't, but I will bore you anyways with my journey. My original order was an 8gb pre-order from the Play Store. That one had major screen raise and flickering. I got a replacement from the Play Store which was unit #2. That one didn't have much of a raised screen but it had horrible flickering.
Once I got that one, I got a full refund from the Play Store. Unit #3 was bought locally at a Staples store. That one had a raised screen and flickering. Unit #4 was my coworker's JR order. That one had a raised screen and in disgust I didn't even check for flickering.
Unit #5 was locally from Walmart yesterday. That one was great! No screen raise and no flickering but the device WOULD NOT charge while the it was powered on. It would charge when powered off though, it was the weirdest thing! That was a problem that I haven't heard of through this whole Nexus 7 debacle. After trying multiple chargers and factory resets, I exchanged it this morning.
Now the one from this morning seems to be the winner! No screen raise or flickering that I can see.