A 6" countertop overhang is too small. The "recommended" overhang for seating is 15". I have limited space in my kitchen and had practically zero counter space, so we ditched our kitchen table and built a separate peninsula, not attached to my perimeter cabs, and gained cabinet storage too. The overhang on my peninsula is 12" and will be a little tight for chairs, but we're tall-ish people and couldn't go any smaller than 12" for leg room. Not sure what your corner piece looks like. If you can post a pic, that would be very helpful.

I declare my bias up front as a disliker of islands. Island lovers will tell you it's worth it to cram them in no matter what, if that's what you want. And we're both right. Unless we're both wrong. But seriously. It's your house. Your bias is the only one that counts. My thing about islands, particularly in small rooms is that they're a hazard to navigation. They're always THERE and you're always walking around them. So my suggestion is, if you must have an island (though I prefer a table, always) then go for a nice, solid MOVEABLE island. Either on lockable wheels, or just one big and heavy enough that it stays in place. Nobody wants a wimpy, tippy island. They come pre-made, or you could have one made custom, or there are pieces of furniture that would serve the purpose. That way, if you hate it, or even if you just have a party, or want to do something in the kitchen that requires a lot of open space, you can just move it off to the side for a buffet or bar station or whatever. You are also freer to make an island like this a little bigger, since you can move it out of the way if it bothers you where it is. It also leaves the "dining or island?" option open to the next owner, and doesn't make it for them. Which I think is even better for resale. Just something to consider.

Here's my take: use what looks best in your space. Also, people love eat-in kitchens. But if they want an island they'll get one. I hate islands. I love kitchen tables. We had an island, original to the house, when we moved in. It was fine. Then we inherited a dining table, versatile enough for the kitchen and with extra leaves if needed, making it better for us than the island. It also looked lovely in the space. Several years ago, we inherited a more formal dining table (from other side of family) and it went in the formal dining room ( which, like yours, had also been a den at one point) . I love having 2 areas to eat-one formal, one casual., I keep hearing that formal dining rooms are going the way of dinosaurs. But I still love ours.

Here is a mockup of an idea for your dining room and living room flip. Obviously, the final placement of the various pieces would depend on their size and necessary clearances/aisles, but this is the basic idea. You only really have two walls where the TV could go, so there aren't a whole lot of options. The orientation I chose makes the wood-burning stove a focus point, which I think is nice. I added a large coffee table between couch and loveseat, assumed a flat screen TV on the wall and added a rectangle in the new dining area to indicate a piece of furniture that could be anything, really (china cabinet, sideboard, bookcase, etc.). As for the kitchen, I went back to the open plan for this drawing. As you can see, having the dining area in the new location makes the seating in the kitchen somewhat redundant, although with kids I'm sure it will be useful. However, I agree with 3littlelights and others that this "open" plan still has you facing away from the open space for most of your kitchen tasks and is therefore not really accomplishing what you want it to accomplish. The layout of the sink, stove and fridge is also extremely awkward. What are the exact measurements of the wall with the sink on it? I know you said the windows were 72x36, but how much wall space is there between them and how much wall at either end? If there is no way to put the fridge on the same wall as the sink, then perhaps something like the plan below would work. It doesn't disguise the posts in any way, but it does give you a vastly better workflow and lets you face the open room while you are working at the sink (you'd want to move the dishwasher to the other side of the sink so it wasn't directly across from the oven).