I can't see from the photos, but if you have enough space above your ceiling, then recessed lighting or potlights would be a great solution. Because you don't have a central island or table, I won't suggest a pendant light.

Do you have a photo of the other light that you are keeping?

Something like this would be my choice - of course I don't know what style you like, but your kitchen is pretty traditional:

drum light

Or something like this, if you can find a mount version, not a swag or pendant:

lampshade style

I'm not a big fan usually of schoolhouse style but I think it could work:

schoolhouse

I'm just suggesting general styles, not these specific fixtures -- I didn't look at their sizes which would be important

That looks like it is pretty close to the cabinets -- would you be able to move the location?

If possible, I would put in a number of can lights. If that is not possible than a flush mount that diffuses the light. (google "flush mount diffuser" and you'll come up with some designs.

For renovation work, you might find Lithonia LED Wafer gives you the look of recessed lighting but is easier to install.

Does your current budget include moving the junction boxes and adding a new central fixture? In my area, that runs about $125-$150 per box if the ceiling situation is pretty easy to deal with.

If moving the fixtures is not in the budget, try picking some new LED track lights that will extend across the full width of the kitchen wall and the refrigerator wall.

https://www.lightingdirect.com/track-lighting-fixtures/c63?term=track%20light