Ok, a couple 1% 100k and 10k resistors plus some caps later, I have a working instrumentation amplifier with gain control! There is some offset error, but I can get rid of that by changing the pot on the bridge. Now I can measure pressure differences of less than 0.5m in altitude (it's better than that but there's a bit of noise because I'm over-sampling the A2D). If I need to improve the performance later, I'll probably get a better chip, or buy a instrumentation amplifier IC. Now all I need to do is figure out why my wireless mouse is interfering with the readings.
This has been really helpful, thanks everyone!
-Z-
Edit: Hey 0008 is out!