I'm hoping to find a purple pigment that preferably, but not necessarily, can be used at room temperature. The goal is a pigment that will break down in septic systems.
There are several such pigments which are bio-degradable by some microbial action (mostly bacterial action) and are oil soluble (lyophilic) and water insoluble (hydrophobic).
chlorophyll : certain bacteria can decompose chlorophyll. A paper citing zoo-plankton activity on chlorophyll is here.
Xanthophylls : This is a general category of several pigments whose degradation by marine bacteria has been widely studied. (You can search for many relevant papers online).
Carotenes : Certain carotenes are also reported to be degraded by fungi and mushrooms. For example here
Anthocyanins (and related polyphenols) which have dark red to purple color are mostly water soluble.
I came up empty for 100% of my requirements. However, I did come up with second best, which is an emulsified purple that mixes well with oil. After mixing, it doesn't leach into any water that contacts the oil.
While it should be possible for anyone to create this, it requires the proper equipment and it is ineffective in a commercial situation when trying to control costs. I found a company that has been very helpful that provides custom samples and commercial quantities at affordable prices. The company is Color Maker.