To relieve some of the confusion remove the clock from between the Windows and change the existing light to a ceiling mount...this clears the space to allow a center placement of lighting over the table to look right...a long fixture will function best....and the size will help establish the dining table as the center of the room...

Consider using 3 fixtures or possible one large fixture

I think one long fixture would work well. This is not a great picture but you should get the idea.

Just came across your question because I have lighting questions too for my weird and cluttered kitchen ceiling. No suggestions for you at the moment, but wondering: Is that magnificent table all one piece (looks like it in the pic) or is there a leaf or two that could be removed? Can't see the depth of the room, but can the table be turned to face into the room rather than across? Thinking, given the current ceiling fixture, that's how it was set up to be in the house design in which case a buffet or hutch would fit on the wall to the right of the windows (a "traditional" arrangement). If the table can't be shortened and if the current placement is your heart's desire, than I think you have to deal with that wall to the right of the windows first because right now, everything looks unbalanced. (The silly vent and fire alarm? don't help but that's really minor - I need to remove two 2x4' fluorescents with a solar tube in the middle and a 16" square vent and ceiling fan in close proximity in a small kitchen). Hope you'll get a lot of good advice but also hope you'll take your time because ceiling lighting is expensive and it can make or break a room. I'll try to tackle that wall as if this were my dining room and share what I come up with it. Good luck.