1µA current noise is way above anything else in the circuit I suspect. Remember its over a 10kHz BW, so its 10nA/√Hz, current noise is normally measure in pA or fA. A 10k resistor has 1.3pA/√Hz thermal current noise for instance, 60dB less.
Of course that noise spec in the TL783 datasheet is probably only a rough/ready thing, perhaps a worst case including bad flicker noise, but still its high - most voltage regulators are not low noise amplifiers. Worth trying to see how bad it is in practice with a real part - can always substitute a 1k5 resistor as a load to compare.