After putting the tremolo springs back in a triangle and adjusting the claw arm spring tension and re-tuning with a tremblock, we've got the Schecter already working better. While zZounds said the best option was to return the guitar for a replacement that's already in perfect working order, the work we've done on it probably puts it in a category of how it should have came to us to begin with.
We may never know if this was a used or refurbished system sold to us as.new or if it was a new system that had major quality control issues with its setup from the factory, but there seems to be no major issues with the guitar after doing a little setup work on it and putting some new strings on.
The body itself seems to be flawless. There is no fret buzz, no sharp frets, and the coil-splitting on it makes it sound like two completely different guitars. Hopefully after intonating is done and pickup height adjustments, she'll be ready to rock.