We have asymmetery in our dining room bc our fireplace is not centered. We had the choice of centering the chandelier in the room or putting it directly in front of the fireplace, making the chandelier not centered in the room. We ended up placing the chandelier in front of the fireplace, but the table is centered in the room. Nobody notices, and I don't either unless I happen to be working on a project in the room. ;) In your case, I'd center the chandelier and medallion in the ceiling relative to the fixed elements in the room. It will be much more noticeable to not have the chandelier centered in your ceiling that your table not centered under the chandelier since there is a separation of visual space between the chandelier and your table. IMHO. Good luck!

yes its done. if you dont want to move the ceiling electrical box right away, 'to do a dry run' you can swag a chandelier to be over your off center table.

I am in the process of removing 1990's ceramic tile from my terrazzo floors (1959 house in Orlando FL) with a hammer-drill. I have a goal each week to tear up 15 sq feet of the tile (and that much fits in my trash can outside). I prefer the not so shiny terrazzo to the ceramic tile. It is a lot of work especially getting up the thinset (I spray water on it to keep the dust down) and to not damage it..Once it is all up and I have some other projects done, I am getting the terrazzo refurbished and it will glow!. I have the same style house and love it. Your tile job is definitely DIY. No pro would have that mess by the kitchen and dining room. I think the potential there is huge. I think the dining room would feel less unfriendly if one could see out those french doors. I'd center the table under the skylight and hang a light inside the skylight. You (a pro) can put a light in a skylight, you just need to affix a board that goes from side to side and the wiring would get run to it in the same fashion it goes to your fan. Ditch the fan. you could hide the wires to the light by making a false ceiling about an inch lower than the present ceiling. You could go with a tongue in groove real wood stained something medium colored. I did that on one of my ceilings. These houses are built with those tongue in groove boards under your layer of roofing. I think those built-in shelving do-dads are really awkward and would get rid of them. They were an add on when they did the 1990's tile. So awkward how the baseboard is that tall baseboard and that era of houses had 4 inch ranch style. Sticks out like a sore thumb wrapped around those wall units. If you can get the glass clear in those doors, remove the shelving, take up the floors, put a light in the skylight and put some plants in there it will look like a different place.

RL's solution sounds like a winner to me. IMO, can lights exist mainly to sell more lighting hardware, because you need so many of them to get something close to even lighting. A hanging fixture or chandelier that reflects some of its light off a white ceiling (indirect lighting) will do a much better job of lighting the room evenly. Using indirect lighting indoors is roughly comparable to reading a book under a nice leafy tree, instead of squinting at it and straining your eyes in direct sun.