Hi,
In my opinion, whatever other problems you have with that circuit - if any, I am not certain devices like the TL431 are at all suitable for wide fluctuations in load. Maybe it's insufficient capacitance or other related, but what stands out to my eyes is the TLC431.
I understood these types of reference (I'm sure it's better to use it and understand it as more a reference than a regulator, it isn't a 7805 etc.) are more usful for setting a reference voltage (or tiny reference current) with ADCs etc. ref pins, or other device ref. voltage pins where there will be no change in load. You could try a Zener in its place.
In my limited experience of experimenting with the 431, I concluded that it really doesn't like changes in load, but is good for ADC refs. And if you think of the datasheet formula, it's for a static condition, and where you can expect x% change with y% change in load as stated in one of the "electrical characteristics" fields (10%, or something like that I think).
Don't remember any "typical application/application hint" schematic for wide change in load, maybe datasheet has one though, you never know.
Good luck!