Currently there is not a way to do this as you have requested in Cascade.
One option you can try is to setup two sets of texture coordinates/textures and on one set one of them check Un Mirror U and Un Mirror V.
Lerp between these coordinates using one of your particle color channels, and a uniform distribution on initial color set to 0,1 with the use extremes box checked.
You can try using the dynamic parameter, with the spawn time only box checked and min max set to 0-1, but there is no use extremes box, so you can get values which are between 0-1 which may look odd.