So, some great progress, and then a hurdle:

I started out with a very dilute dye stain (5 drops dye/4 oz. water/4 oz. alcohol) I then did a follow-up with a similar ratio in just water to deepen the color a bit. The result: Click image for larger version. 

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This wasn't bad -- it's about as much blue as I want, but there was just enough residual yellow from the woodgrain that the result was a slight green tint. I realized I would need just a touch of white in there, which might cut down some grain shape, but would get me closer to the shade I want. So I mixed a batch of whitewash diluted with alcohol tinted with wood dye to my target color and...presto, the result I was hoping for. This did cause a bit of seepage around the cut line, but not enough to get me worried just yet: Click image for larger version. 

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So then I moved on to my second color, a more intense mix of dye and diluted water, only to discover I had missed a glue seam running through the middle of the laminate top. I read through advice here and elsewhere, attacking it with some light heat and scraping, and even broke down to do a bit of extremely gentle sanding with 320/400 grit. So far, I've hidden it to some degree, but its still more visible than I want: Click image for larger version. 

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To be frank, this has me a bit stumped. I either need to find a delicate way of hiding/removing the seam or I may have to switch approaches entirely and go for a different, more opaque finish. Opinions welcome.