Thank you msjoan! It helps to know you had a similar issue. I have told him that is what I want but I am having doubts.

What kind of recessed lighting were you planning on using, those which require separate housings or integrated fixtures that don't? If it's the former, you can use Halo E4RTATSB housings which require 5" or Halo H245RICAT which require only 3-3/4". Of course, there are other brands.

I'd recommend using 4"-or-smaller diameter recessed lights. Those old 6" models look, well, old. Equipped with the compatible housings, the Juno 17 4" round and Juno 17SQ 4" square trim/reflectors are really attractive and available in several finishes.

Pics would be helpful. From your description, it sounds as though you may have 8' ceilings throughout, and in the kitchen they dropped the false ceiling so in there the space has a 7'-4" ceiling or so. If that is the case I would eliminate the entirety back up to the bottom of floor/ceiling joists making a higher ceiling over the entire kitchen to match the rest of the house.

Also, assuming the 3x5 light well is over the middle of the kitchen in the general floor space. Typically you would not light the floors of a kitchen, but the countertops. So placement of recessed can lighting should be based on your counter layout.

I agree 6" cans are dated and not needed . Go 4" all leds 4000K and the spaces will all feel like they are in beautiful daylight and yes to level ceiling to put the cans in .

Thanks all! We are going with 4 inch cans and a level ceiling. They are near or at the edge of the counter tops so as to minimize shadows while working there. Will probably add more cans as it still feels dim in there.