Is there a method for setting up my palette on axes by Hue, Value, and Intensity?
You could mix your fully saturated base hues on one axis, run the desaturated mixes at a right angle to those and if there is room go off on a diagonal with tints of the colors you are using. Alternately just use a different area of the pallet for tints or saturations depending on your preference. 

Other than starting with a cool and warm version of the primary colors I have never heard of a standardized pallet or one that seeks to capture the entire available spectrum. Each artist I know has their own layout and each painting calls for different colors. I think you would be wasting paint and time trying to create a pallet like the color picker from Photoshop, and even in digital painting applications there are multiple areas for choosing by hue, tone or saturation. You just need to find what works for your style through experimentation.