Is there an objective/fool proof way of obtaining the most neutral tones? It would definitely help my processing since I'm mostly doing it by eye (on a monitor that keeps getting inconsistent calibrations on a datacolor spyder3; which despite my best efforts, shows vastly different hues on the two monitors I'm using); I'm not surprised my edits are still off - though I am a little surprised that you are able to pick it out so easily.
This video on color balancing in Final Cut Pro X, as well as
this on scopes cover the concept of color balancing, that can be applied in alternative ways in Photoshop as well.
As jacobolus mentioned using the Info palette is a handy way of seeing how much Red, Green, and Blue there is at a given point. This can be used to take some samples of white, grey, and black areas of the image and see how much color needs to be taken away or added to the channels to achieve a balanced color, with the channels in each range being more matched in number.
Nice thing about Photoshop is there are always multiple ways of doing something, so there's never one sole method. I tend to use either a Curves or Color Balance adjustment layer and reduce or add to the individual channels in the shadows/midtones/highlights to first create a more neutral balance based on the color samples noted, then add any extra changes in other adjustment layers.