That would add a collimating lens, beamsplitter (half-reflective mirror), full-reflective mirror and another photodiode to the setup
Not necessarily - you could simply point the reference detector at the source, as long as you can null-out the absolute difference.
It probably doesn't even matter if it is off-axis of the main beam for the same reason. (a similar system used to be used on early x-ray tomography machines)
Besides, all those things are salvageable from a CD drive
but...if the lightsource fluctuations are reasonably faster than the sampling rate (design goal 20 Hz), then wouldn't one get the same result just by averaging/filtering those out?
It may be - it depends on the nature of the readings and of the fluctuations.