For my money there is no better coloring agent (if I were to color a piece of walnut in the first place) than analine dye, formulated with alcohol
I would submerge it in acetone for nigh onto a week to try and leech out any agents present in the wood that are making it splotchy, and then re-evaluate. (And post pics!)
2 questions: Is analine dye readily available and easy for us mortals to work with?
Will the wood absorb the acetone to a degree that it would affect later efforts to apply the final finish?