Looking at the pix, it looks like the light in the new kitchen will be a few inches lower than the light over the cooktop in the old kitchen. So, maybe, it won't be a problem after all?

Otherwise, the only things I can think of to suggest would be either a valance with the fixture mounted on the back side of the valance or a light with some kind of canopy like an aquarium light (which would probably be very ugly).

have you ck out led lighting..the small lights are very bright..

I found some Xenon eyelid puck lights. What do you think they would look like mounted under the cabinet over the sink with the eyelid turned toward where I will stand?
{{gwi:1595335}} I would use the white to blend with the cabinetry.

I know nothing about Xenon. Does it get really hot? Is it dimmable?

Here is a link that might be useful: Pegasus eyelid Xenon puck

Thanks, Frodo and Ci, for your responses. Frodo, I'm a little hesitant to consider LED lights. Seems I recall that a lot of people on this forum who had installed them were not happy with the quality of the light. I had some of the LED "tap" lights in a bookcase several years ago and the light was pitiful. I think I will let them get a few more years of development behind them before I try them out.