I'd be super curious to see how the accuracy changes with averaging out/low-pass filtering the measurements. Accuracy usually improves proportional to sqrt(N) when you take N samples so your higher precision desire might just be a bit of code to write.

The other side of it though is that you're starting to get down into the "everything needs to be temperature controlled" region as you squeeze that precision number. FR-4 and copper have thermal expansion coefficients around 15-20ppm/C. If I'm doing this mental math correctly, a 5 deg temperature rise would make a 1m long piece of FR4 expand by 0.1mm, or a 10cm piece of FR4 expand by 0.01mm.