My kitchen is smaller than yours (151" x 114", with about 66" of floor space between cabinets on opposite walls). I have three 5" cans along the long counter, each about 4 ft apart (center to center) with the center one approx. midway. Two more cans are along the opposite wall (which is not as long and has the frig and pantry) -- these cans are about 3.75 ft from the first row. The area is very well lit with these 5 cans -- no dark areas or overlap. You do want to center the cans over the counter edges of work zones-- that will illuminate the work area without casting a shadow. If the cans are behind someone working at the counter --> shadow. Also, try to place any can that is in front of a pantry so that the can will illuminate the inside of the pantry, not be blocked by the open pantry (or frig) door. A larger space might look better with 6" cans, but that really is a matter of personal preference. The difference between 5" and 6" is minor to my eye. f you go with 4" you will have to have more of them.

First, I would encourage you to consult a lighting designer before making a final decision on recessed can sizes and types, and placement. Many independent lighting stores have a designer on staff that can help you if you bring in your plans. That being said, your H's plan looks solid, but I would add another can to the left of your sink, given that it will be a prime prep and storage area (but the size of the cans and their spread will help to determine that choice one way or the other). I would also put 4 cans over your island, given that it's a prep & sitting space.

MR16s are low voltage lights that require an external transformer. I personally have never seen them in a house. I have seen GU10, but never seen them as general kitchen lighting. I have one rental that has GU10 in the hallway and it is pain to even find a replacement. I would have to see how this would look in a kitchen. Do you have any links to images of this look in a kitchen? Also, I have gone back and forth on the 4" vs 6" Cans. I have always used 6" cans in the past unless it was for spotlighting. Do you have any links to articles talking about this issue? I will probably go and look at some of the new homes and see what they are using and how it looks. Maybe I can get 5" Cans as compromise, but I don't see them as often.

You want them along the perimeter of the cabinets, about 12-14" from the cabinet doors. Furthermore, you want the recessed lights to be equally distanced from each other. You also want two layers of lights - so the ceiling cans, and also the undercabinet lights you mentioned. Those UCL strips need to be installed toward the front of the upper cabinets. Don't let them install the strips toward the back of the upper cabinets (it's easier to do that, saves them 15 minutes, so that's why they want to). If the undercabinet lighting strips are installed toward the back, they mostly light the backsplash. Installed toward the front of the upper cabinets, they shed light onto the center of the counter where they're supposed to. Make sure all lights are on on dimmers, including the undercabinet lights. Dimmers are not expensive, so this is not a big deal. Make sure the switch for the undercabinet lights are in the backsplash at easy reach. You will want to turn them on while you are working at the counter, so you'll want the switch within easy reach, not having to walk over somewhere to turn on the undercabinet lights.