You didn't tell us much about your glitchey layer but I'll bet that you've applied a Layer Style to it. That breaks the rendering order for 3D. They will still work in 3D you just need to adjust the order. If you need one layer to pass another then you'll need to split it at the frame where they pass and re-arrange the order.
The other option would be to remove he layer effects.
Okay, I changed the order, as you said, and it solved the problem!
I'm still curious to understand this problem better, so I played with the layer orders to try to duplicate the problem with another layer, and I realized that if I put any of the layers on top of the camera/rig layers, they refuse to interact normally in 3d space and instead float on top. I'm not sure I totally get that, since I thought what determines the stacking is it's 3d position in space? You said that it affects the order, so I'm just curious to know how.
I also read about layer styles and as far as I can tell, I have none applied, since the layer is just a .png I dragged in and has no blending mode set. I also tried removing effects, pre-composing, etc., and none of that worked. The only thing was changing the layer order.