Okay, now we are looking at by-pass cap effects.
Here is a base line so that it can be easily compared to the other graphs.

Blue and light Blue is the 56uF cap again. Purple and Green is a 12uF cap. We will be using the 12uF cap for seeing the effect of the by-pass as is it is really hard to see the effect on the 56uF.
Here is the same graph again but I have zoomed in quite a bit on the phase response so we can see the effect.

The Yellow line shows the effect of the by-pass cap. Remember, this is pretty zoomed it. And I tried a .1uF by-pass cap, and a .22uF by-pass cap and could see little to no difference. This is a .33uF by-pass cap.
Note that the difference in phase shift is slight and only in the upper range.
I also noted yesterday, and more so on these measurements, that I had to be very careful not to hold or touch the caps when taking the measurements as the pressure and temperature from my hand can cause some effect. Pressure and temperature can also effect the uF value as well.