Opamp detection of extremely tiny voltage
Spectrophotometers often use a reference beam and a sample beam. The idea is that rather than having to detect these small differences directly in the presence of noise and other (e.g. temperature) fluctuations, only the difference with respect to the reference beam is measured.

So, build two identical sets of your apparatus, and in one of them put a cuvette containing only the solvent. Then use an instrumentation amplifier with large gain to amplify the difference between the TIA outputs of the two devices. Instrumentation amplifiers are fully differential amplifiers, so suitable to measure this small difference in the presence of a large d.c. offset.

Of course, since the two absorption cells will not be completely identical, you will still have a d.c. offset to deal with. But it will be much smaller than otherwise, and you can probably either calibrate it out, or compensate it by adjusting the gain and offset for the reference TIA.