I spent a bit more time thinking about this, and yes you are correct. Each scattering event increases the discrepancy by ~mean free path / atomic radius, which

I spent a bit more time thinking about this, and yes you are correct. Each scattering event increases the discrepancy by ~mean free path / atomic radius, which is about five orders of magnitude. So even starting from a 10^-78 discrepancy, it only takes ~10 collisions to get an order unity discrepancy. I was thinking that the discrepancy due to collisions was negligible compared to the accumulated tidal acceleration, but this is clearly wrong.