If we consider the RC time constant of the power supply:
We have 680 Ohms into 100uF, we have a time constant of 0.068S.
If we look at 8.2K into 22uF, we have a time constant of 0.1804S.
A higher time constant will really shave down the noise, but at the expense of potentially dropping voltage or paying a lot for caps. (I shoot for 0.1S under most circumstances)
8.2K into 2.2uF gives you 0.018S, which isn't stellar, but there are more dimensions to the problem than just the time constant, which is reason enough to give it a shot. Sonically, I'd expect it to be quite good, but you may not be happy with the noise performance (which would be less of an issue with the C4S in the circuit).
-PB