Simply remapping tones or using curves will not create extra measurement precision. It can make tiny highlight differences more visible after capture, but it does not add real bit depth or recover detail the sensor did not record.

For measurements this small, the main limit is not just nominal 8-, 10-, or 14-bit output, but sensor noise and accuracy. If you try to isolate only the top 0.01% of the range, noise will likely overwhelm the signal unless the sensor itself is substantially more precise than its output format suggests.

So the practical answer is: a normal camera is usually the wrong tool for this. What you want is not high dynamic range, but very fine discrimination over a very narrow brightness range. That generally calls for purpose-built scientific/imaging hardware and controlled measurement methods rather than photographic tone mapping or gain tricks.

Reducing exposure and then boosting gain also won’t solve it in a meaningful way, because gain boosts noise along with signal.

In short: no simple camera setting or post-processing remap will turn an ordinary sensor into a reliable 0.01% measurement device near saturation; use a dedicated scientific sensor/system designed for that task.