Also getting new kitchen table and light fixture above it!

If completely redoing the ceiling is not in the budget, then my inclination would be to create a partial white wood drop ceiling in the kitchen over the island by building a flat bottom (level bottom) box (but sides sloped with the ceiling) the size of the countertop of the island above the island so you can move the box for the light within that box and hang the light fixture centered over the island within that box.

Yes, a chain is the simplest solution, but not visually pleasing and reminds me of my mom's kitchen! It can be an interesting detail, or painted out like the ceiling. Here's some inspiration pics showing same solution as above with pics: Hope this helps.

#1 Sheetrock box - size of island - against the slope of the ceiling - center the light over the island - can add other lighting

#2 Simple stained wood to match existing cabinets - tight to slope of ceiling

#3 Entire kitchen ceiling to follow slope - add lighting as necessary in position

#4 Bring ceiling "box" down over island with simple detail - paint as ceiling

#5 Decorative to match cabinets - same size as island - drop parallel to island, do not slope

Loving all of these ideas - thank you so much! He has a good friend that he trusts that is an amazing carpenter and I will show him all of these photos (and I agree I hate those chain lights)! Everything in that house is so dark. His LVP floors are peeling (terrible builder quality) so we are going to lighten those up. New kitchen table - we can do a lot with just a lighter paint, fixtures, table, etc. He really wants our help and is ready to get started!

I would not put a pendant back there, this room look like it could use more light. I would install good looking track or a rail light with adjustable heads. This will also let the new dining light be the star of the show. The island is pretty small and doesn't really need attention drawn to it, lighting up that whole room would serve the space I think. building out a box on this ceiling would just magnify the scale of the island.

Fabulous idea! It is so dark in there. No light above the kitchen sink. No under cabinet lighting. I will show him these photos. Thank you!

you can add under cab too. they make styles that link together and only need one plug.