I agree put in as much as you can. We have 16 6 in. cans on 4 different switches, with dimmers, so I can light up everything or just one side or just the middle. Also have 1 pendent over DH's sink and 2 over my sink. One bigger light over the table in the middle of the kitchen. The hood has 2 halogen lights plus we put in a solartube opposite the window wall. Everyone told us it was overkill but in the dark of winter I can light up the kitchen like we are outside in the summer. LOL. Almost all are double switched with the bank of main switches to the right of my sink above the trash pull out cabinet. The placement of the lighting was one of the hardest thing we did in this remodel. I measured and moved the cans for days before the drywall went up. It was worth it in the end just remember to have the middle of the cans out about 10 in. form the upper cabinets, plus molding, so they shine down on the counter without any shadows. It was hard because one side of the kitchen has 30in.base cabinets and the other side has standard 24in. but with a bump out for Dh's sink and some of my upper cabinets are 14in. deep. Claudia

You could attempt cove lighting ( a form of indirect lighting where the light is directed upwards to the ceiling). For instance, lighting could be placed on top of the beams.

Thank you everyone for your thoughts and advice. I know I created this problem out of ignorance. To be honest, under cabinet lighting didn't even enter my mind until after everything was already done and I saw how dark it is and when, in another thread, someone else mentioned they have Blue Pearl Granite and installed LED under cabinet lighting which made the blue chips in the granite really pop. When I first thought about adding the lighting I assumed the power source would be created inside the cabinet which meant the backsplash already being installed wouldn't be an issue. But, after doing some research online I see it can be added to wall outlets and switches. It's kinda looking like I'll be stuck with battery operated lights or no lights at all. :(

I used the phillips EW Powercore LEDs, Nice quality light (high CRI is essential in a food preparation area lest your pork chops look like they came from zombie pigs) and very easy to install. So small you don't see them if you mount at the front edge of the cabinets. You can just daisy chain them using plug-in connectors that are available in a wide variety of lengths.