The table is heavy, but very nice. I'd try to lighten up the chairs too to help balance things out. Can you show a pic of the MCM chairs that you like? I'm a fan of eclectic. Perhaps you can make them work in here by tweaking the styling a bit.

New Chairs will not fix it, you don't want to use a spindle chair with a heavy wood table. The chairs around it in the photo are balanced well for it. Not only is the wood thick on that table, but its very dark, and the room has dark elements to it as well. If you want a different look, then that table will have to go and I'd suggest painting the walls a lighter color (not gray) as well

I was thinking something like one of these maybe (but with dark wood)

Agree it would be ideal to start over, but may not be practical right now.