I wonder if that marginal non-linearity is problematic, though. See e.g. Lumileds datasheet for LUXEON 2835 product family (a fairly randomly chosen white power LED), page 13: quite linear relationship between current and light output, which only loses tracking somewhat at low levels. Again, I doubt it would be a problem for this experiment.
PWM is indeed straightforward, but does not solve your relevant remarks on effective illumination of a sample which also depends on e.g. angle of incidence and the radiance pattern of the emitter. However...we can tell from the perfboard prototype that apparently the use of a fairly diffuse light source is considered, and that would deal with this particular concern fairly well.
The main issues remains: can it be expected that the bio-sample responds differently to pulsed light vs. continuous light? Fact of the matter is: we don't know. I've seen people in this thread taking a stab at it, but I find that kind of conjecture very doubtful. On the one hand, we know of several processes that seem to "don't care" about pulsed vs. continuous. On the other hand, I certainly know of chemical processes where there IS a difference (see e.g. reciprocity failure in photography). Where the photo-sensitive processes inside bacteria fit here, we just don't know. For a research setting, I think it would be very risky from a methodological viewpoint to just assume it doesn't matter.