I looked it all over again today and I think I found the main culprit. The spindles were both bent, the passenger's side was worse than the driver's side. I pulled them both off and straightened them out. Before I reinforce them, I figured I'd bolt them back on to see if that improved matters, and it did. It's still not 100% perfectly centered, but it'll do for a 6 year old (this will be my daughter's kart). Tomorrow I'll add some gusseting to reinforce them so hopefully it won't happen again. If it does, I'll build a beefier set sometime later down the line
Another thing I found was that although the front shocks look the same, one is around 1/2" shorter than the other. I guess I'll worry about that later; for now I need to worry with getting it running so she can actually ride it.