I inadvertently "lost" a conversation
on this same subject this past weekend -- didn't note her name. That
lady didn't want a swag. She had two different ceiling levels in her
great room. I tried to find that thread but could not. Was that you?

To center an overhead light that is not centered where you want it
you may need to create a faux ceiling -- a shallow square wood box only
deep enough add a new box between the box and the ceiling to be attached
below the existing ceiling. This box would be placed in the center of
the new location where you want the light fixture and the new light
fixture would be affixed to the center of that box.

The box would need to be large enough to cover any indication on the
ceiling that the original light fixture was at a different place and,
preferably, it would need to be at least as wide as your new light
fixture.

I don't have two different ceiling levels, so it wasn't me. But while I'm on here, I will attach a photo of what was done to fix our light problem. The ceiling was scraped down into an oval to conceal the circle and we bought an oval shaped light fixture.The flat ceiling paint in the oval matches the flat finish that surrounds the ceiling around the room and joining the kitchen, so it worked out well.

I don't think you are going to solve the problem by changing to a flush fixture.

If you choose to provide a new rectangular area below the existing ceiling, I might suggest that you differentiate that rectangular area by, say, giving it a smooth texture to contest with the of the larger ceiling, and perhaps build a reveal around the perimeter to make it appear as if that lowered rectangular area is not connected to the main ceiling, i.e., it appears to float below it, so the design looks purposeful, rather than as an afterthought to solve an unforeseen problem. The size (length and width) and proportion of that lowered rectangular area ideally should be related to the size and proportions of the table below.

I hope things work out for you as hoped.