What about under cabinet lighting?

You don't have to do recessed lighting, you just have to get rid of the florescent lighting.

There are tons of really nice LED track systems which IMO are a much nicer choice than recessed in a kitchen that is narrow and I agree some under cabinet lighting is always good BTW 6” cans are really outdated and not need to have good lighting with LED s

Can you post a pic of the full kitchen, not just the ceiling? I might do one row down the center, then put a single recessed can above the sink. Or you could also do a pendant over the sink, too.

Keep a pendant or flushmount over the breakfast area. (Assuming the current flushmount is over a table, but can't tell.)

and what ever bulb you are using in that semi flush, throw it in the trash and go get a bulb the same (I'm hoping) warm (2700k) bulb that will match the cans you bought.

do you really need a table in this room?

I’ve got 3 little ones (6,4 & 2) and they can be a bit rough on tables. It is definitely crowded but I haven’t found a good (fast/easy) way to protect my vintage dining table from fork stabs and seat cushion stains :-/

You think I should nix the table in the kitchen and figure it out?

Return can lights. Do undercabinet led lighting and explore track (new style) lighting. Best to have 2-3 different kinds of lighting in a kitchen. Yes, remove that table. Need more pictures to give better advice.

IMO LEDs in any room should be in the 3500-5000k rane to keep colors true and whites white most of my clients go with 4000k range. Yes to moving the table and as I mentioned no to 6” cans .

A pedestal table with straight legged chairs, not splayed out like your current set, will save you lots of space. Under counter LED lights and a track lights above would be my choice.

Yes to no table. and the track idea is a good one as well, and maybe more cost effective to install.