Bummer... and I can imagine the frustration.

I'm afraid I don't have any revolutionary suggestions. All I can think of is maybe using the goof off in conjunction with some P320 sand paper (???). I only suggested 320 because it's finer than 240 and coarser than 400. No technical reason, other than trying to avoid going through the veneer.

Another alternative, given the major glue spot area is at the edge, is spraying a burst on the edge with paint to cover the glue. You could use a dark brown paint for the burst in keeping with your existing theme.
I don't know what your plan is/was for clear coat, but if you did the burst idea, you can use an acrylic paint and [apparently] you can apply polyurethane safely over acrylic. I have not done it, but I read a few articles that say it's doable.

Sorry that's all I got...