I found this photo online, perhaps it will help. In this picture the crown molding on the cabinets flow from the kitchen to the adjoining room. Maintaining continuity with the color and some of the trim detail will make the rooms transition nicely. Don't overlook the details like hardware finish, lighting and plumbing fixtures as these elements can also tie the two styles together. I hope this was helpful.

A nice whitewash wall/paint treatment would brighten it up if done in a light color. Or I would paint it but not sure if all the knots will bleed through? If so then I would use an oil base Kilz to stop bleed through and paint it depending on the interior design I want for each room. I would not paint the ceiling for a more Montana look,

You can of course have a furniture repair business add material and refinish. Or you can add a center accent piece of tile, or wood inlay. If you're going from a narrow rectangle to a square, you would need to disassemble the table anyway, might as well do something fun with it.

I'd love your advice - Where would be the best placement of my appliances, sink, oven etc? I would love to have my sink under the window - do you think it could work?