Jane
Welcome to NCWW.
I am no expert, with little walnut experience and no veneer experience. In any case, I do not see what you describe in the photo - the colors gradually shift from the sapwood to the heartwood, but I do not see (color) splotchiness. Naturally photos do not always show what we can see in person. Could you somehow highlight an area where you see this? I do see sheen differences (how reflective the surface is), especially the glossy area at the top middle portion, whereas most of the surface appears low sheen (matte).
If it is parched areas (are they the same areas you describe as splotchiness?), that is often related to the finish. You might try
1. Test on some scrap. Finishing schedule and experiments should be done 1st on scrap, through the whole sanding, staining, clear coating process - which I say but only rarely do.
2. More layers of brushing lacquer for a hopefully thicker and more consistent layer thickness. Can't do this on the finished piece as you have sanded off the 1st attempt.
3. Or brushing on coat or two as a sanding sealer, sand back to the wood surface (but not really removing much or any wood, just the finish coats), and then recoating. THis second option is what you are in the middle of, you just haven't recoated.
And I hope you are working in a well-ventilated space when using brushing lacquer - that stuff makes me dizzy in a hurry! (even dizzier than normal).
Please post more as you discover more - love to see the finished piece in its entirety.
Hopefully others can weigh in here.