The 3 cans right and left of the stove are a good idea, as are the four cans in the next row. Though you need lots of light for your daughter's needs, I suggest that you use dimmers on everything to balance the room. Have you considered using a drop-down island light instead of the 3 cans over the island? In "entertainment mode" if you dim your other cans and raise the level on the island light, you draw people to the island. You could go "high-end" with this one fixture to set a complete design tone for your kitchen (think Hubbardton Forge - http://www.hubbardtonforge.com/ProductsInfo.cfm?Design=137525 but with "opal glass, which is actually opaque white Or you could spend less with something like the Kichler fixture (see link below). Here is a link that might be useful: Kichler island pendant

I have noticed in a couple of lighting threads recently people recommending that the cans be placed 10" or more off the edge of the counters. I am not an expert -- but my lighting store expert told me to place them just over or only a inch or so off the counter edge. I did that and it seems to be perfect. The counter is well lit without glare and no shadows. However, on the other side of the room the lights are place farther away because of the pantry and frig, and on the one little patch of counter next to the frig (used only as a landing spot and home of the phone) the farther away light does cast a significant shadow when I am standing there. My 800 lumen LED discs are placed starting 14" from the end wall, which positioned them where they can illuminate the first upper cabs without being blocked by open doors, then approx. 52" apart down the length of the room (140" from wall to cabs across the end wall, so 3 lights). I've 2 rows in my kitchen which is only 9.5ft wide (approx 6.5 feet between the upper cabs). This has given me excellent illumination with no dark or glaring spots. I am not sure, but I think that maybe when I chose the lights, I went to the manufacturer's website (Sylvania) to get info on how wide of an area the units would illuminate. Hope that helps some.

@apple_pie_order The all white kitchens in my idea books also have wood floors which help to warm things up. Unfortunately, I was unable to talk hubby into wood floors for the kitchen so I had to go with tile which brings even more white into the mix. The furnishings are mine but the upholstered items will be recovered in a different fabric. I am not sure what to do with the furniture at this point since the furniture wood colors are so warm. I have toyed with the idea of another table and credenza but I am not sure I want the expense right now.

Sometimes the way the room is arranged suggests that pendants aren't necessary or contra-indicated. I don't have pendants over my island, just two recessed lights and I don't have any desire to add pendants when I remodel. There is plenty of light in the room. IMO, you would be better off putting a chandelier over the dining table and not having pendants in the kitchen. Just rearrange and add to your recessed lights to cover the area more evenly. It looks like six should do it. Is there an extra one in the middle row because of where the island used to be? When you install LVP, make sure you don't make it impossible to get a dishwasher in and out of the spot for it since the level of the floor is going to be raised. The previous owners of our house did that, except they trapped it, and now we can't pull it out to service it.