I also love your hutch. Can you use it for another purpose in another room, perhaps? If not, I think you could do a fair amount of trickery with some curtains. Treat your two windows as one and put one large shade over them, perhaps one of those twiggy bamboo ones. Then pretend the window is where you want it to be and hang your curtains as such. The curtains will barely reach beyond the window on the right side and on the left, they will be covering up quite a bit of wall, but only a little bit of window. Does this make sense? Then swag your chandy over the table like you said.

The hutch is a beautiful piece, but does pose a problem for the dining room. Can you move it into another room on a focal wall and use it as a bookcase? Your beautiful painting will fit better on the wall where the hutch is now, and maybe you could find a small server with a mirror over it to reflect the painting to put where the painting is now. There really isn't room for furniture on the hutch wall and still be able to pull out the chairs if the table is centered.

A plant in the corner, as Barbara mentioned, could balance the space. I feel the room is just off-balance, rather than off-center due to the large hutch on one side dominating the room. Moving the hutch elsewhere is also a simple solution as well. Besides, I doubt you'd want someone hitting the back of their chair against the glass!

someone had a similar problem and 1 of the replies came back with this post, that I thought was interesting. If it were my house I would probably treat it as 1 window meaning that the curtains on the right side would sit over more of the window than on the left. http://rebecca-gatheryeroses.blogspot.com/2012/01/ill-take-curtain-number-two-dealing.html
Good luck!

Is the room wide enough to allow you to line up the middle of the table with the left hand edge of the window? Love the hutch but off-setting your table might help to balance the room. Visualize a window scarf draped over the windows and hanging part way down each side.

Otherwise what about a diagonal placement of the table? I would place the back corner of the table into your open corner by the door way and slant the rest out towards the living room and hutch. It would still leave a walking path and access to the chairs. Any movement that doesn't make it look like it should be centered on the window since that lack seems to bother you.

Or just take out a leaf and make the table smaller - turn it sideways? Move out to the living room more, put an extra chair or two by the window with your little cabinet/table.

Trying to think outside the box here and uncenter everything.

This may sound weird, but could you remove the table leaf and turn the table perpendicular and butted against the wall where the painting is? Personally, I'd rather have the hutch, which looks like a converted armoire to me, as a focal point in a living room, library or foyer.

I wouldn't even try to center it. Keep it the the way it is and just put an eye-catching painting on the wall in front of the hutch, which is lovely, by the way. You can also try placing a long, slim, but nice console with a beautiful flower vase, and maybe a chair on either side.
Another option would be to move the hutch to another place and turn the table 90°.
And last but not least, if it really bothers you, maybe a round table could be an option.

Thank you everyone for your wonderful ideas!