Can we see the ceiling?

Almost exactly this but the recessed cans is what I don’t prefer about this design

Here are a several photos. In these photos, when tape lights are used, all the "boxes" are lighted. I think it would look weird if you lit only some of them.

Perhaps the best solution would be to center recessed lights in the boxes. If you arranged them in a pattern, you would necessarily need to have a light in every box: perhaps lights in box 1, 3, 5,... in the first row, then 2, 4, 6,... in the second row, etc. These Nicor 3" shallow, canless recessed lights might fit. Or maybe it would be better to use low-voltage canless lights to simplify wiring by eliminating the need for Romex and a power supply at each location.

-- amateur