Update: looks like this is entirely affected by the model's scale. If I double the model's size, the issue is made worse by a huge factor (I'm talking the entire vehicle glows). If I halve it, the problem is gone completely. Doing this either through the exporter or within blender itself seems to produce the same effect, and again, applying scale to ObData does nothing. Unfortunately though, making the car smaller is obviously not a possibility for me, so I'm still stumped!
EDIT: Fixed! Turns out this is caused be scaling too generously in object mode (what isn't?). To fix it, I scaled everything down in object mode first, then went into edit mode and scaled each object back up individually. Not sure whether the old "add a cube, join the meshes and delete cube" method would have worked though.
Well, thanks for the help anyway!