There's not much chance that your ceiling will remain undisturbed when you take that out. A builder will have to take a look and tell you what needs to be done, to repair or replace. A better solution would be recessed lighting around the perimeter. Use 4 inch cans and, if budget permits, LED units that are dimmable. Talk with a good lighting showroom and electrician to get the best results for your project.

Once you remove the light fixture, there would be a tendency to demolish the entire dropped ceiling.

Not afraid of doing some ceiling work. Wasn't sure if when I removed the plexiglas, wood frame and florescent fixtures how recessed cans would look up in that space itself. It's about a 50 x 72 area, 7 inches deep. I like the idea of the cans over the counter shown but would need more general lighting. I would love to take the whole ceiling to the roof line like the main living room but the wife doesn't want to sink a ton of money into a house she wants to eventually downsizing from. See new photo.

You would need to post a measured drawing to figure out how many and what kind of light output you'd get from cans. They wouldn't necessarily be contained in the area where the light is now, and you wouldn't necessarily need anymore lighting in the room. Good/correct placing of recessed IS good general lighting.