Stu, you may get some good responses here, but I encourage you to try the kitchens forum and lighting forum as well, where there are people are more into kitchen design and actual lighting. Myself, I had a lighting designer who was invaluable in making sure there was good enough lighting that I'd be willing to cook at night. ;)

You say the tray is over the island. Does that mean really most of the kitchen? Or is it a narrow recess just over the island?

When you're asking about recessed lighting in the perimeter, do you mean in the lower portion outside of the tray? Or around the edge of the recess? What and where would be lighted?

I have indirect for my main kitchen lighting, but recessed lighting at key spots around the room, mostly so that the cabinets will receive some light at night. That's in the corners, and in front of the pantry cabinet, which is the middle of one side. On the other three sides it wasn't necessary--one is coolers and ovens, one has the baking counter but there are no uppers there so the corner light covers it, and one has the cooktop and sink which each have their own lighting. That's in addition to the overall bounce lighting, strong down lighting on the island, and undercabinet lighting.

I don't use the recessed corner lights very often, but when I need them, I need them and I'm grateful to have them. Whereas, I really don't need the undercabinet lights because the rest of the room is so well lit and there aren't uppers over most of the work surfaces anyway.

OMG! Thank you pillog! Not sure how I ended up on the appliances forum, but I do appreciate your response and your comments!