Will,
As you know,I'm strictly a harware guy,so I can't quite conceptualize your plight fully,but I will say that 6 stereo inputs on a mixer is a tall order-especially on a budget!
However though,the good news is,I think I may have found the ideal mixer for you...
The Soundcraft Compact 10 mixer.It has 6 stereo inputs & it's geared towards computer based recording-very impressive for a mere $249.00(USD)
From what I've read,the Compact series have decent sound quality for them being an entry level line and they are well reviewed mixers by many.
In the past,I have shopped around through countless brands & I honestly don't think you'll find anything more reasonably priced than the this Soundcraft series(unless you go with-perhaps Behringer,but I would'nt recommend them).
Hope this helps.
Thom