My objection to cans is that they provide zero indirect light. All the light is directed downward, regardless of the beamspread. Working under cans is much like working in direct sunlight - the combination of bright light and strong shadow stresses the eyes. Working under well-done indirect light is like working in bright shade or under a partly cloudy sky. The even lighting is much easier on the eyes. Lighting designers knew that 70 years ago. Some of the original installations in the homes of that era are still in use by old-house fans. They're easier on the eyes than modern cans, even though the total luminous flux may be lower. Most modern lighting designers seem to work around this limitation of recessed lights by installing very large numbers of cans. However, that fix results in much higher installation costs, more energy use for lighting, and greater heat loss through the perforated ceiling. Cans are fashionable and some people like them because the source of light isn't visible. They also excel at highlighting room features. However, they are not a very practical system for task lighting and general illumination. An older friend of mine had her new house built with cans. Within months after moving in, she complained that she couldn't see well enough when working in the kitchen. She eventually had the electrician come back out and install a surface mount fluorescent fixture over her work area. Now she's happy. :)

Could we see some closeup pictures of the tiled box out window over the sink? I want to do this with my window and I've gotten nothing but stanky side eye from every person I've told but I know in my heart of hearts it would look gooooood!

"We are taking down an extra large square fluorescent light and replacing it with one two-bulb type flush mounted light and maybe another if need be then also adding a pendant over the sink." It will depend on the size and layout of the kitchen. One flush mount will not work as good as the fluorescent for two reasons. (1) The fluorescent puts out 6.5 times as much light. A 4' fluorescent with 4 tubes (2600 Lumens × 4 = 10400 Lumens) A two bulb flush mount w/60 watt bulbs or equivalent (800 Lumens × 2 = 1600 Lumens) (2) The surface mount fixture's light source comes from exactly 2 points that are very close together. The fluorescent light source has infinite sources of light within that 2' × 4' area which spreads the light out better, causing less noticeable shadows. With the fluorescent, the light reflecting off of all the other surfaces in the kitchen is also bouncing off at a more infinite number of angles, (compared to just from the pinpoint light source of the standard fixture) further contributing to the feeling of even light in the kitchen. . Pendant lighting that is bright enough to really contribute to the overall lighting of a room will also be glaring, since it is down closer to eye level. Pendants are fine for specific task lighting or mood lighting. Under cabinet lighting can also be a bit glaring if it is relied upon for more than half the light needed for a task. Keeping the under cabinet lighting out close to the face of the cabinet helps. Using two surface mounted luminaries on the ceiling will help spread out the light sources and help the light bouncing off of the cabinets light the room more evenly. Whether I would use fixtures with two or three bulbs depends on how big the kitchen is, how much light you are used to, and how intricate your tasks are. 800 Lumens × 6 bulbs is still only 4800 lumens, or less than half of what you currently have. You could try taking out two of the tubes and living with it for a while to help decide how many fixtures you want on the ceiling. . The difference between two 3-bulb fixtures and recessed cans over the outside edge of the countertop should not be enough to worry about as long as you have the under cabinet lighting and the pendants. There is a trade off between the two types of lighting. The recessed lights can be put right where you need them, but the light does not spread out as evenly. The surface mount in the middle of the room can produce more unwanted shadows, but the light spreads out and bounces off everything better to counteract the problem.

Yes, it will be "fine" ....but it could be better, because most of the light will be illuminating floor space instead of the the front of the counters/stove (where most of your work takes place, so you generally want that as well lit as possible) or the cabinet interiors. Undercabinet lights will have to overcome the shadow that will be cast by having the ceiling lights behind you, so you have less illumination than you might - and still, only if you make sure that they are installed at the front of the cabinets, not back next to the wall as most contractors will do. That is what the lighting design pro that I paid for emphasized to me. It will be very easy for your installer follow that plan, but just position the lights over the edge or just off the edge of the counters. He will just have to use a few inches more wire for each light.