I don't have a great solution to this, but I toyed with three different approaches and then settled on this one as the least intrusive...
https://www.buildyourownguitar.com.a...?t=5339&page=6
I used a piece of maple to make a fillet that I glued onto the side of the neck to make a smooth transition. I ultimately used a solid color paint on the neck, and the good news is that it looks pretty good. I did not quite match the color of the maple, so I am sure it would be more noticeable if I had stained.
An alternate approach that I considered was to put some filler around the veneer, and sand until the top is smooth, and cap the "step" with a piece of veneer. That would probably not stand out as much if you are staining...but would leave a "step." Not a big deal, but I decided I didn't want a step.
I also rejected making something out of binding material for the transition. This could work if you don't care that the binding is only on one side. You would make the piece, glue it in and sand it like the fillet. Alternatively you could make the cap out of binding material. It would not be hidden, but might look like a design feature. Since it's physically impossible to look at the top-side and bottom-side simultaneously, it's unlikely that anyone but you would notice that the top and bottom are different.